How to Cut a Square Cake Starting 2 in. from edge, cut a horizontal line across your cake. Slice approximately 1 1/2 to 2 in. pieces of cake. Serve this row first before continuing to cut.
Can you cut a round cake into small pieces?
In addition to the typical method of cutting a round cake into triangle-like slices, round cakes can also be cut into small square pieces, smaller triangle slices, and even long, thin strips. One method was even designed by a scientist to ensure every piece of cake is fresh and moist.
How do you cut the perimeter of a cake?
Well, the perimeter of the cake is 24”, and there are three pieces, so each piece will get 24/3=8” of perimeter. We start making our first cut to the center, then count around the perimeter 8”, make the next cut, then repeat. It’s as simple as that; divide the perimeter, make sure each piece has the same linear length, and cut to the center.
How do you cut the perimeter of a cake?
Well, the perimeter of the cake is 24”, and there are three pieces, so each piece will get 24/3=8” of perimeter. We start making our first cut to the center, then count around the perimeter 8”, make the next cut, then repeat. It’s as simple as that; divide the perimeter, make sure each piece has the same linear length, and cut to the center.
How to Cut a Square Cake
Cake is the nicest part of any celebration, but for those who are entrusted with the responsibility of cutting the cake, it may be a stressful experience!Slicing a cake into neat, even pieces may be a difficult task, and if you’ve ever worried about reaching cake-cutting greatness, you need not be concerned anymore!The following cutting tutorial, ″How to Cut a Square Cake,″ will demonstrate how to cut and serve your square (or oblong) cake quickly and efficiently.No more guessing – this procedure is effective regardless of the size of the cake being sliced.
- Starting 2 inches from the border of your cake, cut a horizontal line across it
- Approximately 1 1/2 to 2 inch slices of cake should be cut
- Serve this row first before proceeding with the rest of the cutting
- 2 inches from the edge of the cake, cut another horizontal line across the surface.
- Using the same procedure, cut 1 1/2 to 2 inch pieces and serve them before cutting another horizontal line
- Continue in this manner until the entire cake has been sliced
- This approach also works for sheet cakes that are 9 x 13, 11 x 15, and 12 x 18 inches in size. The following are some extra techniques and strategies to make slicing and serving a cakewalk: Pour hot water over your knife after each slice if you are cutting a dense cake to avoid the knife from adhering to or ripping up the cake.
- If you’re cutting a frosted cake, wipe the knife after each cut to ensure that the pieces are beautiful and clean
- To achieve even slices, split your cake into even portions using baker’s twine or unflavored dental floss before cutting it into slices.
- Before cutting your cake, set it on a grip pad to keep it from slipping.
Is your cake a little too cool to be square? Check read our page on How to Cut a Round Cake to discover how to acquire party portions for cakes that are 8 inches or bigger in circumference. What additional cake-cutting advice do you have to offer? If you have any tips, please share them in the comments below or on Instagram with the hashtag #wiltoncakes!
How to Cut a Round Cake
Article to be downloaded article to be downloaded It might be tough to cut round cakes into enough pieces for everyone at times because they are such delicious treats to begin with.Other options for cutting round cakes include small square pieces, smaller triangular slices, and even long, thin strips, in addition to the traditional way of slicing round cakes into triangle-like slices (see illustration).One approach, which was developed by a scientist, ensures that every slice of cake remains fresh and moist to the touch.
1 First, choose a knife that is large enough to cut through the entire round cake.The length of your knife should be at least as long as the circumference of your round cake, for instance.If you are unable to locate a knife that is as long as the circumference of your cake, use one that is as long as feasible instead.Alternatively, if your knife isn’t long enough to go around the whole circumference of your cake, you’ll have to glide the knife over the top of your cake in order to form a clean line in the frosting.
2 Before cutting your cake, soak your knife in warm water for a few minutes.Fill a large glass half-full with warm running tap water.To use your knife, place it within the glass of water and lean it up against the rim of the glass.Wait until you’re ready to cut the cake before removing the knife from the water.
As soon as you’re ready to cut the cake, carefully remove the knife from the glass and wipe away any remaining water with a tea towel.You’ll want to make sure that your glass is tall enough to accommodate the knife you’ll be using for this project.
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- 3 Make a slash across the centre of the cake with your knife using your knife. Holding your knife above the cake with both hands is a good technique. Hold the handle of the knife with your dominant hand and the tip of the knife with the fingertips of your non-dominant hand. Knife the entire cake, cutting through the center of the cake with your knife. To score a straight line across the cake, rock the knife from tip to handle in a circular motion from the tip to the handle. Simply press your finger into the frosting to score a line, but only until you reach the first layer of cake! Make sure you don’t cut into the cake itself.
4 Make a second line that is at a 70-degree angle to the first line you just scored.Begin the second line in the middle of the first line, and so on.Slice at a 70-degree angle to the first line with your knife, resulting in a slice that is around one-third of the half of the cake or one-sixth of the entire cake, depending on your preference.The first two lines of code have now split the cake into three equal halves.
- The smaller triangle was divided in half by a third line drawn across its center. One half of your cake will appear to be made up of two triangles, one of which will be bigger than the other. From the centre of the smaller triangle, the third score line should split it exactly in half, according to the rules. The four parts of the cake have now been cut out using the first three lines. The size of all four final portions will be determined by the two tiniest pieces.
6 Divide the bigger triangle into three halves by scoring two more lines.The following two score lines will be used to divide the bigger triangular piece into three portions that are all the same size.From a technical standpoint, each of the five triangular pieces that are formed should have an about 36-degree angle on the diagonal.The whole procedure is dependent on guessing the size of the slices, but the goal is to make all of the portions of the pie the same size as one another.
- 7 With your knife, stretch the four half-lines across the top of the cake. One-half of the cake has now been divided into five pieces with a knife. Only one of the lines that has been scored so far spans the complete circumference of the cake. Four of the lines that have been scored so far are barely half-way across the sheet cake. Make use of your knife to extend those four half-lines so that they run the length of the cake’s circumference. It is possible to divide the round cake into 10 even pieces as a consequence of this process
- if you are serving more than 10 people, you may cut each of the 10 pieces in half to get an additional 20 even pieces.
- 8 Cut your cake into 10 equal pieces by cutting it along each of the score lines on the cake. In between each cut you make in the cake, dip your knife into the warm water and wipe it off with a tea towel. Make a cut across the entire cake with your knife, following the score marks you’ve created before. Each slice of cake should be cut from the center of the cake. Pulling the knife out of the bottom of the cake carefully is important to success.
- Scoop up each piece of cake with an offset spatula once it has been sliced, or wait until the entire cake has been cut before beginning to dish out cake pieces.
1 Soak your knife in water for a few minutes before you begin cutting the cake.Place your knife in a glass or container filled with warm tap water.Set the glass or container aside.It should be kept stored in the container until you are ready to slice the cake.
When you pull the knife out of the water, wipe it down with a tea towel to remove any remaining water.Please make sure that the glass or container you select has a height that is appropriate for the knife you intend to use.
2 Cut the spherical cake into long, thin strips using a sharp knife.Each strip should measure approximately 1 inch (2.5 cm) in width.As soon as you’ve cut a strip of cake off the cake, put it flat on a cutting board or plate to cool.Make sure you re-heat your knife between each significant cut.
If you don’t need as many slices of cake as you originally planned, you may make the strips wider or longer.
- 3 Cut the lengthy slice into 1-inch-wide (2.5-cm-wide) pieces. Once the lengthier slice has been laid flat on a cutting board, use your knife to cut it into 1-inch-wide (2.5-centimeter-wide) strips. Upon completion, you will get a slice of cake that is 1 inch (2.5 cm) thick and 1 inch (2.5 cm) broad, with a length that is equal to the height of the cake. It is not necessary to warm the knife in water before cutting these little strips
- you may also cut the flat slice into strips that are longer than 1 in (2.5 cm) if you so choose.
1 Before you begin, soak your knife in warm water for a few minutes.Allow your knife to soak in a glass of warm tap water for a few minutes before you begin slicing the cake.As soon as you remove the knife from the water, wipe it off with a tea towel to remove any extra water.Between each large cut in the cake, re-warm the knife in your hands.
With a heated knife, you can cut through the cake more quickly and easily than with a cold knife.
- 2 Cut a circle in your cake 2 inches (5.1 cm) from the edge, then place it in the center of the cake. Insert your knife vertically through the cake at a point that is approximately 2 inches (5.1 cm) from the edge. Maintaining a vertical position with the knife, cut a circle in the center of the cake that is 2 inches (5.1 cm) from the edge all the way around the cake. The result is that you’re effectively generating a new round cake in the centre of your previous round cake.. It is only possible to use this approach for cakes with a diameter of at least 8 inches (20 cm). Smaller cakes should be cut into the traditional triangular shapes
- the end result will be a ring-shaped cake on the outside and a circular cake on the inside.
3 Cut the ring-shaped outer cake into 1.5 in (3.8 cm) broad pieces, as shown in the photo above.Prepare the knife by re-heating and drying it before continuing.Make individual pieces of the outer, ring-shaped cake about 1.5 in (3.8 cm) broad using the knife by cutting the outer, ring-shaped cake in half.In the case of an 8-inch (20-cm) cake, this will provide 21 pieces that are all the same shape and size.
Depending on the size of the cake (greater than 8 inches/20 cm), you may either retain the same slice width of 1.5 inches (3.8 cm), which will result in more than 21 pieces, or you can increase the width of each slice to still produce around 21 pieces.
- 4 Cut the smaller circular inside cake into triangular pieces using a sharp knife. After removing the 21 outside slices of cake, you will be left with a fresh, but smaller, circular cake to cut into pieces. Begin by slicing the inner circular cake in half horizontally across the centre. After that, cut the cake in half again, this time at a 90-degree angle to the last cut. It is possible to cut each quarter part in half (which will result in 8 slices), or you may divide the sections each quarter section into thirds, which will result in 12 pieces, depending on the size of your inner cake and the number of slices you want. Using the above example, if the entire cake is 8 inches (20 cm) in diameter, you will have a 4 inch (10 cm) mini-round cake left in the centre. Remember to rewarm and dry your knife before you begin cutting the inner cake. You will not, however, be required to rewarm between cuts.
1 For cakes that will be kept for a long period of time, use this scientific procedure.This strategy is most effective when you have a circular cake that will not be consumed in its whole at once, such as at a party or gathering.In the event that just a little piece of the cake will be consumed, and the remainder will be preserved in the refrigerator for later consumption, this is the procedure that will offer you with the freshest cake on a consistent basis.It was developed by a British mathematician named Sir Francis Galton and initially published in the magazine Nature in 1906, when the approach was first used.
- 1 For cakes that will be stored, use this scientific approach. This approach is most effective when you have a circular cake that will not be consumed in its whole at once, such as at a party or celebration. In the event that just a little piece of the cake will be consumed, and the remainder will be preserved in the refrigerator for later consumption, this is the way that will offer you with the freshest cake on a consistent basis day after day SIR Francis Galton, a British mathematician, invented this approach in 1906, and it was published for the first time in the magazine Nature that year.
3 Make another incision in the cake, this time 1 inch (2.5 cm) to the left of the initial cut.When you make the second cut, you will have a long, thin slice or strip of cake that will cut straight through the centre of the cake.Even though it is only one inch (2.5 cm) broad, this piece of cake will extend around the whole circumference of the round cake.If you choose, you can cut a slice that is wider than 1 in (2.5 cm) if you so desire.
- 4 Make a thin slice of the cake with your knife and remove it from the pan. Slide your knife under the cake, just beneath the tiny slice that you made with the first two slices. Do not cut through the cake. Carefully lift the knife to allow you to carefully remove the thin slice of cake from the center of the baking sheet. Serve and/or consume the thin slice of cake that you cut out in the centre
- if you’d like, you may chop this central slice into smaller pieces.
- 5 Bring the two ends of the cake together and fix them with a toothpick. Using your hands (or a spatula or knife, if you prefer) gently slide the two ends of the cake together to form a tetrahedron in the center of the cake dish. Check to see that the interior pieces of the cake are contacting one another on the inside. Glue the two ends together to keep them from unraveling. The original method recommends wrapping a rubber band around the cake to keep it in place. It is important to note that technique will only work if your cake has a tougher shell made of something like fondant (and isn’t too large)
- otherwise, it will fail.
- Alternately, you may tie the two ends together with a piece of ribbon, parchment paper, or a piece of plastic wrap to keep them from unraveling.
- You might even skip sealing the cake altogether because merely sliding the two ends together would have likely been sufficient to secure the inside of the cake.
- 6 Make a second slice from the centre, this time perpendicular to the previous slice. When you’re ready for another piece of cake, remove it from the refrigerator and cut another slice from the center of the cake. The slice should be cut at a 90-degree angle to the initial slice this time, though. Then, using the same method as before, slide the ends of the cake together to store the cake for the night. The choice of whether or not to cover the cake with a lid or plastic wrap when storing it in the refrigerator is entirely up to you.
- It is important to note that the inside of the cake, or the sponge, will remain fresh because none of it is exposed to the air during this technique of baking.
7 Repeat the process until the cake has been consumed in its entirety.Every time you want another slice of cake, simply follow the same procedure as before.For each time you repeat the process, rotate the cake another 90 degrees to ensure that the slice is sliced in a different direction every time.In order to ensure that the two ends are always nearly the same size when they are slid together, do the following: Eventually, the bits of cake that are left will be tiny enough to be eaten on their own, and you will no longer need to cut portions from the centre of the cake.
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Things You’ll Need
- A round cake or several round cakes
- a long knife
- a tall glass
- warm water
- a tea towel
- an offset spatula
- a rectangular cutting board
About This Article
Summary of the ArticleX When cutting a circular cake, use a knife that is as long as possible, and immerse the knife in warm water prior to make it more easily cut through the cake.Using the knife, score a line across the middle of the top of the cake’s icing with the tip of the knife.Then, at a 70-degree angle from the first line, score another line to form a triangle with the first line.Create two smaller triangles by scoring another line in the space between the first two lines.
Repeat the technique around the entire cake, dividing it into ten equal pieces in the process.Finally, cut through the cake along each of the lines you marked with a sharp knife.Follow the instructions below to learn how to cut a circular cake into square pieces.Did you find this overview to be helpful?
Thank you to all writers for contributing to this page, which has been read 59,019 times so far.
Cutting a Square Cake
Synopsis of the pieceX Utilize the longest knife possible for slicing circular cakes, and immerse the knife in warm water before cutting to make it more easily cut through the cake.Making use of the knife, score a line through both the center of the cake’s top and middle of its sides in the icing.Then, at a 70-degree angle from the first line, score another line to form a triangle with the first two lines.Create two smaller triangles by scribbling another line between the previous two.
Repeat the process around the entire cake, dividing it into ten equal pieces in each direction.Final step: Cut a horizontal slit through the cake along each of the lines that you marked.See below for instructions on cutting a circular cake into square slices.Were you able to benefit from this overview?
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Consider the following scenario: we have a square cake with each side measuring 6 inches; how do we divide this into three equal pieces?Here are a handful of examples of how this may be accomplished: How did we come up with these reductions?Because the cake has a 24″ circumference and is divided into three parts, each slice will have a 24/3=8″ circumference on average.We begin by making our first cut to the center, then count around the perimeter eight inches, making the next cut, and repeating this process.
The process may be summarized as follows: split the perimeter into equal-length pieces, check that each piece has the same linear length, then cut to the center.The fact that the perimeter extends around a corner is immaterial, provided that there is a continuous 8″ of perimeter for each component of the puzzle.As a result, depending on where the initial cut is made, there are an endless number of continuous solutions to consider.Each piece having the same linear length of perimeter has the effect that, if the cake has icing around the edges on the sides and top, each piece receives the same amount of frosting.
When we cut the cake into three equal strips using two vertical straight cuts instead of three equal strips, the central portion would be deprived of the edge frosting.You can now understand why it’s critical that we cut straight through the middle!It makes no difference how many pieces we need to produce.It’s the same strategy as before.
- As an example, consider how the cake would look if we had to divide it into five equal halves.
- The circumference of each edge is 24/5=4.8″ in this case.
- The answer is straightforward and lovely in its simplicity.
Why does this work?
This method appears to be a bit too simple.What causes it to work?Remembering our geometry lessons from school, the area of a triangle is equal to half the base multiplied by the vertical height of the triangle.Each of the triangles in the picture below has the same area since they all have the same height and base, as shown in the image below.
Consider slicing the cake into a plethora of triangles, all of which have the same foundation (same distance around the perimeter).Every triangle A–D in the picture below has the same height (i.e., the perpendicular distance from the edge to a line through the center is the same), and they all have the same base (as shown in the image below).Each of the triangles A–D has the same area as the other triangles.In a similar vein, you can show that the areas of triangles A and Z are identical.
In reality, because the square is a regular polygon, any triangle that has the same base on the border and a vertex in the middle will have the same area as the square itself.No matter how a triangle ″wraps″ around a corner, the result will be the same.Because the altitude of both partial triangles is the same, the area of each is simply proportional to the length of the linear edge.
In the event that you know a talented baker who can produce standard n-sided polygonal cakes, this technique will still work.The perpendicular distance between each of the edges of a regular polygon and the centroid is always the same in the same direction.Use our ″tape measure around the perimeter″ approach to equally distribute a special dessert!(When taken to its logical conclusion, you can see how this simplifies to the same technique that we use for a round cake, as well as how the interior angles are the same).
It is possible to picture scaling up and down the size of the cake (based on the origin at the centroid), and you will find that this approach is not affected by the thickness of the icing (providing the icing is of uniform thickness all the way around).Each piece of cake and side icing should be divided equally among the people who cut it.(Drawing a line between a cake with and without frosting reveals that the only difference is the icing.) Okay, I’m starting to get hungry…
Simple techniques for slicing them to perfection.9 separate cakes must be sliced in different ways.This is step 1.The following are a few simple principles to follow while slicing basic cake shapes so that you don’t wind up with crumbs.
2 out of 9 Measure out the amount of pieces you’ll need before you begin cutting any cake.To do so, score the slices first by softly outlining the areas where you’ll be cutting with a knife.3 out of 9 Using a long, thin-bladed knife and a gentle sawing motion, slice layer cakes into squares or rectangles.4 out of 9 When slicing light and airy cakes such as angel food or chiffon, use a serrated knife and saw to cut through the cake gently without deflating the airiness of the cake.
5 out of 9 When slicing cheesecakes or other dense desserts, it is best to first rinse the knife in very hot water to prevent sticking.This will aid in preventing the knife from adhering to the cake or damaging it.6 of 9 Wipe the knife clean after each cut to ensure a more perfect slice.7 out of 9 Cut parallel slices across the breadth of a square or rectangular cake while making a square or rectangular cake.
- Afterwards, cut the cake in half lengthwise and crosswise across the first set of slices.
- 8 of 9 Ideally, you should have portions of cake that are of equal size and form — which will make everyone delighted.
- To learn how to do anything, watch a little video.
- 10 of 10 Continue Reading to see an advertisement.
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Cutting a Square Cake Equally – The Math Doctors
We’ll be looking at a few ″dissection problems″ during the next few of weeks, which will require cutting a form in a variety of ways.We’ll look at a problem that turns out to be rather straightforward, despite the fact that it appears to be complex at first glance: cutting a cake into pieces that have the same quantity of cake and the same amount of icing on each piece.So that you may find it at your own pace, I’ll start with a handful of responses that provided only suggestions and work my way up to complete solutions.
The first question is from 2001, and it is as follows: a square cake cut into five equal pieces Ravina’s birthday cake is in the shape of a square.The length of the side is 20cm.She would want to divide the cake into five pieces, one for each of her four friends and one for herself, and she plans to do so.She intends to utilize straight vertical cuts to create five pieces of similar volume, and she will employ straight vertical cuts to accomplish this.
Consider the following scenario: Ravina makes the initial cut from the center of the cake to a spot in the upper left corner.If she starts with the middle of the cake, where does she need to create the other four slices?I haven’t even gotten started yet.To be honest, I wouldn’t even know where to begin.
Please, someone assist me!We’ll be seeing numerous different variations of the problem, the most basic of which is as follows: We’ve been informed how big the square is (but not how tall the cake is), and we’d want to divide it into five equal pieces.It is necessary to produce wedges that meet in the center, rather than four slices parallel to the side, as we would assume (particularly if two people want the majority of the icing!).In this case, the height of the cake does not matter; the volume of each slice is proportionate to the area on top.
- The only difficulty is: how can we identify the most appropriate locations?
- I responded quickly, only making a suggestion: Hello, Katie.
- A excellent way to start is to consider the area that will be covered by any slice cut from the cake, such as this: ————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————— As soon as you’ve done that, consider about the area of a wedge that travels around a corner, such as the following: +-+ ||
|/||/||You will discover that knowing the distance d along the outside of the cake is all you need to know, and you can use that information to get the proper value of d for which each piece equals one-fifth of the cake (see Figure 1).The solution is shockingly straightforward!The area of the triangular piece may be calculated using the formula (A = fracbh = fracdcdot 10 = 5d) as shown below.
The area of a wrap-around piece may be conceived of as the product of two triangles added together.For the time being, I’ll leave you to consider the remainder of your options.
Equal volume and area!
Two months later, we received an inquiry that was quite identical to the first, but with one extra requirement: Using a square cake to divide it into five equal pieces If you have a square-topped cake that is a rectangle solid and is frosted on all faces, how do you split it into five pieces so that everyone gets the same amount of cake and icing?All cuts must be made perpendicular to the surface being worked on.I’m at a loss as to how to proceed.All I can do is split the cake into four equal pieces and eight equal pieces.
Please assist me or provide me with a method through which I may attempt to resolve this situation.Still, vertical slices are required, since this avoids certain deception; however, we must ensure that the volume (cake) and the quantity of surface area (icing) of each piece are the same for each piece.That appears to be a somewhat greater difficulty.Pam has most likely employed symmetry to create four or eight parts that are all congruent and, as a result, have the same volume and area as one another: But, of course, you can’t achieve it with only five pieces.
I responded once more, this time with a hint that was more or less the same: Hello, Pam.This problem is less difficult to fix than you may expect.I recommend that you begin by thinking about wedge-shaped components in the following manner: • • • • • • • • • • • • • • • • • • • • a If you want to go any farther, you may make wedges that wrap around a corner like this: s +-+ ||||
|/+ |/|b +-+-+ a +-+-+ a +-+-+ a +-+-+ a +-+-+ a +-+-+ a +-+-+ a This area may be found by drawing a line from the center to the corner of the rectangle, dividing it into two triangles, and then calculating the area of each triangle.I believe you will have a decent notion of what to do when you have completed this task.This time, let’s take it a step farther than before.We weren’t provided exact lengths in this case, so a broad description is all that can be expected; nonetheless, we’ll stick with the 20 cm side lengths from the first challenge for now.According to the variable we have here, the area of a triangular piece is (5a).
- Similarly, the area of a quadrilateral piece is ((5a + 5b = 5(a+b)), which is still 5 times the amount of perimeter utilized by the piece (the d in my first answer).
- This is the most important concept.
- In order to split the area of the top of the cake into five equal parts, each portion must be a minimum of 80% of the total area of the cake (400text2 times 20text2 = 400text2).
- We discover that the distance down the side must be 16 cm when we use the value (5d=80).
- Furthermore, because each piece will have the same distance along the circumference, they will all have the same amount of icing on top as well as around the sides of the piece.
The answer, with details
At the conclusion of that response, I made reference to the following response, which was given in 1999 and which we may review now: Using a square, cut it into five equal halves.Hello, Dr.Mathematica.I was wondering if it was feasible to cut a square cake into five equal sections without using a knife.
You cannot slice the cake into 10 sections and give two pieces to each guest, and the cake must be cut through the central point.There are certain limits, though.||||
It was they that were rejected, rather than what I had done.|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||Could you please assist me?Thank you very much, Doctor.The first effort does not make use of the center; however, the second try is exactly what was specified — assuming that the dimensions are correct.It’s important to note that we’ve returned to a question that isn’t concerned with the frosting, despite the fact that the solution is.
Doctor Rob responded as follows: Thank you for reaching out to Ask Dr.Math.Your latest drawing, which is seen above, conveys the correct concept.Make a note of the length of the sides of the square, which will serve as the cake’s base.That’s what we’ll call s.
- The square has a perimeter of 4s, which equals its area.
- Take that number and multiply it by 5.
- Now, beginning from any place (for example, the middle of the top edge of your picture), measure around the edge a total distance of 4s/5 times over and over again.
- Make a note of this location and measure around the perimeter again for a total distance of 4s/5.
Continue in this manner until you reach your starting place.Make cuts to each of the five locations specified starting from the center.This will divide the cake into five pieces of identical volume, and in addition, each piece will have the same quantity of frosting as the other four pieces.Consider what this looks like when (s=20) is used, as was the case in the first question: In this case, the perimeter is 80, thus we moved a fraction of that distance from one point to the next, i.e., a fraction of 20 = 16 between points.
I numbered each side in tenths on each side (2 cm).That, therefore, is the solution.Is this, however, correct?It is sufficient to demonstrate that the areas of the four quadrilaterals and one triangle are all equal in order to establish that the volumes of the components are all equal.Create the square’s diagonals by drawing lines across it.The quadrilaterals will be divided into two triangles each as a result of this.
All nine triangles will have a height of s/2, and their bases will be s/2, 3s/10, 7s/10, s/10, or 4s/5, depending on the number of sides.Starting at the origin and working your way around the perimeter of the square, you’ll see that s/2 + 3s/10 = 4s/5 7s/10 +s/10 = 4s/5 4s/5 = 4s/5 s/10 + 7s/10 = 4s/5 3s/10 +s/2 = 4s/5 s/10 + 7s/10 = 4s/5 3s/10 +s/2 = 4s/5 s/10 + 7s/10 = 4s/5 Using our example, the individual bases are (AB = 10 + 6), (BC = 14 + 2), (CD = 16), (DE = 2 + 14), and (EA = 6 + 10), all of which are 16 cm in length, and the total length of the base is 16 cm.If you start at one corner and work your way around the perimeter of the square, you’ll see that s/2 + s/2 = 3, 3s/10 + 7s/10 = 4, and s/10 + 4s/5 +s/10 = 7, and s/10 + 3s/10 = 7, and s/10 + 3s/10 = s.
Each side contributes to the total of (s = 20).On this diagram, we can see how the five parts have been divided into nine triangles, as well as how they are all at the same altitude.The area of each triangle is given by the formula (A = fracbh = fracbcdot fracs = fracbs).As a result, the triangular areas will be s2/8, 3s2/40, 7s2/40, s2/40, or s2/5, respectively.When you tally up the areas of the triangles to get the areas of the quadrilaterals, you will find that all quadrilaterals have an area of s2/5, or one-fifth of the total area of the square: s2/8 + 3s2/40 = s2/5 7s2/40 +s2/5 7s2/40 2/40 = s s s s s s s s s s 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2/5 s2/5 = 2 2/5 s2/40 + 7s = 2/5 s2/40 + 7s 2/40 = s s s s s s s s s s two-five-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-thousand-th 2/8 = s2/5 = s2/8 Now, the volume of each of these polygons is equal to the area of the cake multiplied by the height of the cake, thus all volumes are equal to hs2/5, and all icing areas are equal to (4h+s)s/5.
- Because each piece has a volume equal to its area multiplied by the height h of the cake, they are all equal, (fracs2); and the icing on each piece is equal to the area of the top of the piece multiplied by the area of a rectangle with width fracs and height h.
- Take note that if you had started at a different point, such as a corner, the quadrilaterals would have different shapes, but the area of each would still be s2/5.
- This is because the triangles forming them have a common altitude of s/2 and the sum of their bases is 4s/5, so the total area is A1 + A2 = ab1/2 + ab2/2 = a(b1+b2)/2 = (s/2)(4s/5)/2 = Similarly, any starting point may have been utilized for the same reason.
Here’s an example of a cake with the initial cut made at a corner:
How about 13 pieces?
Now, it’s interesting that all of these queries were about five pieces; we’ve received a handful with various numbers as well, which is unusual.What if there were a total of 13?Consider the following query from Jim, which was asked in 1998: Cake Dividing – A Mathematical Puzzle You’ve got a nine-inch square cake on your hands.It is a two-layer cake with a buttercream frosting.
One and a half inches is the height of each layer.Each layer, as well as the sides, are coated with a quarter-inch-thick coating of icing.The bottom of the cake does not have any icing.How can you split a cake into 13 pieces so that each piece contains precisely the same quantity of cake and icing by making straight knife slices through the cake?
After the pieces have been sliced, they may be reassembled, but no cake or frosting may be removed from the pieces.With precise measurements and the condition that both cake and frosting (also known as icing) be divided evenly, this is the most thorough version of the issue that we have.The proportions aren’t really necessary, however the thickness of the icing will cause a minor problem.Doctor Wilkinson responded by saying, ″This is a really excellent puzzle.″ If you wish to continue working on it on your own, I’ll provide you with a handful of pointers to get you started.
- Please let me know if you have any questions or if you just want an answer.
- 13 is an excessive number of pieces; it is difficult to visualize the problem with such a huge number of pieces.
- Try a lesser number, such as 5 instead (4 or 2 would be too easy).
- If the cake were round rather than square, it would undoubtedly be simpler to make.
To split the circle into five equal halves, you would simply mark off spots on the circumference that would divide it into five equal parts, then cut from the center of the circle to the points marked off.Now try to replicate the process with a square cake.″Try a lower number″ is a common piece of advise when confronted with a difficult subject.Can you understand why the number 5 is the greatest option?A classic solution is to ″try a simpler but comparable problem.″ For example, wondering ″what if it were round?″ can lead to the idea of splitting the perimeter evenly, even though it would not seem like it would work at first glance.
- Jim responded, expressing his desire for more than just a clue (without explicitly stating that he truly requires more than a hint!): Thank you so much for taking the time to respond.
- These suggestions are quite beneficial.
- I believe I understand how to approach the problem, but I would appreciate it if you could email me an explanation of your approach.
- Doctor WIlkinson answered in the following way: The tip I offered you was actually quite useful, so thank you for that.
- All you have to do is be brave and follow the instructions to the letter.
You may ensure that all of the pieces of cake and icing are identical by dividing the circle of the cake into 13 equal portions and then cutting your way around the cake from the center out to each of the 13 spots on the circumference.Notice first that the amount of cake in a piece is just the area of the piece’s top multiplied by the thickness of the cake.This will help you understand what I mean.If you want to know how much frosting to put on your cake, multiply the area of your cake by its thickness.
If you want to know how much frosting to put on your cake, multiply its thickness by its length times its thickness times its thickness.If you want to know how much frosting to put on your cake, multiply its thickness by its length times its thickness times its thickness.Using the circle as a guide, divide it into 13 equal parts.You’ve now completed your icing on the side, and all that’s left is to make sure that each piece has an equal amount of surface area to finish the cake and apply frosting to the top.Because we are cutting through the icing at an angle, the pieces on the sides are not quite rectangular, and as a result, their breadth is not exactly proportionate to their height.You can see an example of the problem here: Those pieces that are closest to the center have a wider angle, resulting in trapezoids that have a somewhat larger surface area.
However, the conventional puzzle implies that the frosting is extremely thin (maybe just a gloss), which reduces the severity of the difficulty!If you divide the cake in the manner I advised, you will have two types of pieces: triangular wedges and pieces that go around the corner of the cake (see photo).The area of the triangular parts equals one-half the product of the base times the height.All of the triangle pieces have the same height since the distance from the center to edge is the same for all of them, and the base is one of the equal divisions of the circumference, which means that the base is the same for all of the triangular pieces as well.I’ll leave it to you to consider the situation of the parts that go around the corners, but they do work as well.
- Here’s an illustration:
What about the angles?
We’ll conclude with a challenge using only three pieces; by now, you should be able to figure out what to do, but what if you had to figure out the angles to use for the cuts?This question comes from 2001 once more: Using the Rule of Thirds to Divide a Square I’d want to take a square and divide it into three equal portions by drawing three lines radiating from the center of the square from one side to the other.It was found that in order to complete a circle, each line must have an angle of 120 degrees.The challenge is in ensuring that the square’s areas are all the same size.
As opposed to the previous two questions, this one does not include a cake and does not make reference to the equivalent of frosting; instead, Frank is obviously thinking about the fact that three sectors of a circle with center angles of 120° will be equal.Which angles would a square have if it were a rectangle?Doctor Rob responded by starting with the same concept that we’ve seen multiple times before and then calculating the angles from there.For the sake of simplicity, he employs a coordinate system with each side measuring two units in length: Frank, thank you for taking the time to write to Ask Dr.
Math.There are a variety of approaches that may be used to accomplish this.Here are two examples: A(-1,1)GB(1,1) o-+-o A(-1,1)GB(1,1) o-+-o ——————————————————————————————————————————————————————— H + – – – – o – – – – + I |/.O||/.|
- o-o-+-o D(-1,-1)FJC(1,-1) The first method is to draw a straight line from A to O.
- Then the areas of AGO and AHO are both equal to half a square unit each.
- That indicates that the areas of GBEO and HDFO must both be 5/6 square unit in order for ABEO and ADFO to have a total area of 4/3 square unit each.
The remaining areas of OEI and OFJ are 1/6 square unit, which means E must have coordinates (1,1/3) and F(-1/3,-1) and F(-1/3,-1).Then:
Tips & Ideas from Butterflake Kosher Bakery
|Cake Cutting Guide – A PerfectSlice Everytime With all the unique and amazing cakedesigns available today, below are tips on how to cut different shaped cakesinto uniform slices. Also, check out the Wilton website for more helpful information oncakes. Wedding cakes are usually cut into 1 x 2 inch slices. Beforecutting the cake, remove the top tier. This is usually saved for the weddingcouple’s first anniversary. Then start cutting into the 2nd tier, next 3rd tierand so forth. Party Cakes are typically cut into 1 1/2 x 2 inchslices. Tips Have a long thin knife and cake server ready.|
- Pour hot water on the knife and slide the knife smoothly through the cake while slicing it
- After you make your initial cut, dry the knife to prevent it from disintegrating.
- In order to maintain a flawless cut every time, wash and dry the knife between each slice.
- Make a faint mark on the cake to ensure that the slices are evenly spaced.
- Lift each slice of cake onto a plate or into a favor cake box with a cake server or spatula
- repeat with the remaining slices.
How do you cut a round cake into 10 equal pieces?
Then, using your knife, extend the four half-lines across the top of the cake. Make use of your knife to extend those four half-lines so that they run the length of the cake’s circumference. The end consequence of this procedure will be the division of the circular cake into ten equal portions.
How do you cut a round cake to make the most servings?
This is how you should be cutting your cake, according to tradition: To get the most out of your cake, start by cutting two slices through the centre of the cake, one on each side. After that, you may cut the large slice into smaller pieces for the rest of the group to enjoy. Reassemble the cake such that it is still a round once you have done this.
How do you cut a round cake into 12 pieces?
Start by cutting the cake into quarters, then each quarter into thirds, following the numbers on a clock as a reference. If you want to make 12 even slices, start by cutting the cake into quarters, then each quarter into thirds. In order to make a flawless cut, pull the knife out from the side of the cake rather than raising it through the top of it.
How can you cut a cake into 8 pieces with 3 cuts?
Cut1 – Make a vertical cut along the middle of the cake, resulting in two equal halves. Cut2 – Make a horizontal cut through the center of the cake, resulting in four equal slices. Using the third cut, go through the centre of the cake and slice all four pieces in half, resulting in eight equal slices (four equal tops and four equal bottoms).
What do you say when cutting a birthday cake?
What matters is that you have fond memories of the event. So, please join me in singing a happy birthday song and cutting the cake while we wait for the cake to arrive. (Insert name of birthday boy here): Today is a very special day for you, and we wish you a joyous celebration of your special day. Cake, love, and gifts topped off a wonderful day.
How do you cut a cake into 7 equal pieces?
Divide the perimeter of a square cake into 7 or 9 or n equal lengths if you wish to slice a cake into slices that are 7 or 9 or n inches long each.
How do you cut a cake into 6 equal pieces?
A straight line drawn across the center of the circle using a ruler should be drawn next. There are three lines that must be drawn to split the circle into six equal sections, and this is the first of them. Throughout your design, every line, including this one, should pass through the center of the circle exactly once and divide two of the six inner ″flower petals″ in halves.
How do you cut a pie without it falling apart?
Step 1 — Place the pie in the freezer for 15 to 30 minutes to allow it to cool completely before cutting. The fruit pie should be kept refrigerated, but it should not be frozen. Step 2 — Score the crust with a large serrated knife to make it more decorative. Gently push the knife across the top of the pie, cutting through the edge of the crust as it passes through it.