Introduction: Archimedes's Circumscribing Pi-Cake

Picture of Archimedes's Circumscribing Pi-Cake

A sphere has 2/3 the volume and the surface area of its circumscribing cylinder. It's a beautiful, magical relationship, that I wanted to show off. This pi-cake is made with a sphere of French silk pie (crust and all) stuffed inside a cylindrical white cake with whipped cream frosting. It is delicious and amazing to cut into at any Pi Day party!

Step 1: Supplies

Picture of Supplies

White Cake - 
- 4" tall cake pan with 8" diameter, one or two is fine, depending on what you have available
- cookie sheet
- 3 boxes of white cake mix
- oil, water, and eggs, amounts depending on what the cake mix requires
- cooking spray

French Silk Filling - 
- 2 cup butter, softened
- 3 cups white sugar
- 10 tablespoons unsweetened cocoa powder
- 3 teaspoons vanilla extract
- 1 tsp finely ground black pepper, optional
- 8 eggs, room temp.

Pie Crust - 
- 2 1/4 c flour + more for rolling
- 1 t salt
- 3/4 c shortening
- 1/4 c capacity measuring cup
- 1/3 c capacity measuring cup
- 1 c capacity measuring cup
- 2 c capacity measuring cup
- kneader
- rolling pin
- pastry blanket for rolling out the dough
- foil
- all metal sieve with diameter just barely smaller than the cake pan
- kitchen twine

Whipped Cream Frosting - 
- 1 16 oz. tub of whipped cream, defrosted
- 1 16 oz. tub of whipped cream frosting
- wax paper
- tubes of writing icing

Step 2: Make the Cake

Picture of Make the Cake

To make the cake cylinder, you will make two 8" diameter cakes that are 4" tall each. If you have two identical cake pans, that makes dividing the batter between them easier. I didn't, but my cakes still turned out pretty even.

Typically box mixes come with cooking times / temps for 2 8" round pans. According to the Joy of Baking website (http://www.joyofbaking.com/PanSizes.html), deeper pans result in less evaporation (probably due to less surface area), so you need to bake longer at a lower temperature so as not to burn the cake. I baked mine at 310 degrees for 80 minutes.

1. Spray your pan very liberally with cooking spray.
2. Preheat the oven to 310.
3. Make all three cake mixes with their appropriate oil, water and egg proportions.
4. Pour about half of the batter into the cake pan. Batter should be about 2/3 of the total volume of the cake pan.
5. Put the cake pan on top of a cookie sheet and then into the oven. The cookie sheet will save you a lot of clean up time, if your cake rises too much and drips over the edge of the cake pan.
6. Cake is done when a toothpick or knife inserted in the center comes out with only a couple crumbs on it.
7. When the cakes come out of the oven, let them cool completely before you remove from the pans. I let mine rest overnight. You could also speed up the process by putting the pans straight into the refrigerator for an hour or so.

Step 3: Make French Silk Filling

Picture of Make French Silk Filling

The filling for this pi-cake is just two batches of a regular French silk pie recipe. I made these two batches individually and then put them together, instead of trying to make one large batch. I've tried to do that in the past when making multiple pies, but the resulting filling doesn't have the right velvety texture.

Once you've made two batches, you can put them together in one large container and keep in the refrigerator until the cake / pie crusts are ready.

To make one batch of the French silk filling:
1. Beat 1 cup of butter and 1 1/2 cups sugar until well creamed. This should take about 5 minutes.
2. Add 5 tablespoons cocoa powder and 1/2 teaspoon pepper and beat well.
3.  Add 4 eggs, one at a time, beating several minutes after each. I blend about 3 minutes after each egg. By the end of this, step, there should be very little graininess from the sugar in the filling. 
4. Sample often for quality assurance.
5. Beat in 1 1/2 teaspoons vanilla extract. I use Mexican vanilla, which is twice as strong as regular vanilla extract, but more vanilla in this recipe isn't a bad thing.

Step 4: Prepare the Cakes

Picture of Prepare the Cakes

After the cakes have cooled completely, you can prepare each to be filled with pie crust and filling. Make sure this is done before you bake your pie crusts.

1. Remove the cakes from the pan. No need to level the cakes if they're a bit domed. The extra height helps. 
2. Flip each upside down. Using a knife, score a circle about a half inch deep about half an inch smaller than the cake on all sides.
3. Now start digging. I preferred to do this with my hands, as I was able to gentle scrape the cake innards out without marring the whole cake. 
4. You'll want to pull out cake scraps until you have a nice half sphere that is the perfect resting place for a French silk pie.
5. Reserve the cake scraps and combine them with leftover French silk filling for a yummy mush. Wait. What? I didn't do that.

Step 5: Make Pie Crusts

Picture of Make Pie Crusts

To make the pie crust sphere, you'll make two circular pie crusts and shape them to cover the outside of an all-metal sieve covered in foil. The sieve should be all metal so it doesn't melt when you put it into the oven.

1. Take a piece of foil, about 12" square, and use it to cover the outside of the dome of the sieve. Fold the edges of the foil into the the cup of the sieve. Preheat the oven to 350.
2. Cut a piece of twine long enough to extend from one edge of the foil dome to the other. This will be your measuring tool for rolling out the crust.
3. Sift 2 c flour in the large measuring cup and sift 1/4 c flour into a 1/4 c capacity measuring cup.
4. Pour the 1/4 c flour into a 1/3 c capacity measuring cup. Gently lift enough flour from the 2 c into the smaller cup to make the 1/3 c full.
5. Put the 1/3 c into a small bowl. Prepare the 1 c capacity measuring cup with 1 cup of ice water.
6. Put the 2 c flour (just shy) into a big bowl with 1 t salt & gently, just barely fold in.
7. Fill the now empty 2 c measuring cup with 1 1/4 c of water & add enough Crisco to make 2 c total (using water displacement to make 3/4 c Crisco). Pour out the water & put the Crisco in with the flour / salt.
8. Cut with a knife until the Crisco is decently covered in flour.
9. Start kneading with a kneader until it makes 1 large formation. Seriously, keep kneading.
10. Add 1/4 c of ice water to the 1/3 c of flour to make a paste. Add the flour paste to the kneaded ball.
11. Use a knife to cut aggressively just until the paste is mixed in. Just cut 3 times, flip, cut 3 times. Do not overmix. Cut in half.
12. Flour the rolling pin and rolling surface. Cover one half of the dough with some flour & shape into a disc. Roll the dough out into a circle with a diameter that matches the length of your piece of twine.
13. Place the rolling pin on the rolled out circle. Lift the towel to drape half of the crust over the rolling pin. 
14. Place the sieve, opening down, next to the rolling pin. Lift up the rolling pin to transfer the dough to the sieve.
15. Shape the dough nicely to the sieve. If the dough extends over the side, just trim the edges. There will have to be some fold over on the edges as well to make it fit nicely. 
16. Pierce the dough dome a few times with a fork. Place it directly onto the oven rack, opening down.
17. Bake the dough dome for 6 or 8 minutes to par-bake it.

Step 6: Make the Frosting

You can use whatever frosting you'd like for this recipe, but I chose whipped cream, since a layer of whipped cream is the classic topping for French silk pie.

Take the softened whipped cream, combine it with the whipped cream frosting, and mix with a spatula to make a light frosting. It will be a nice complement to the pi-cake, but sturdy enough to use for decorating.

Step 7: Assemble

Picture of Assemble

1. When each pie crust dome comes out of the oven, place it carefully upside down into the prepared cake.
2. In order to remove the pie crust from the foil-covered sieve, you may need to unfold the foil and then lift out the sieve and foil from the crust.
3. Let the crust rest a minute or so, then you can gently push it down into the opening so it's a perfect half-moon.
4. Fill with French silk filling. Resist checking for quality control. It's fine.
5. Take each half of the pi-cake and put into the freezer for at least 30 minutes.
6. Remove the halves from the freezer.
7. Select your bottom half. Put some overlapping layers of wax paper around the edge of your cake plate or serving dish, and place the bottom half on top of it. At this step, I used writing icing to add the formula of the volume and surface area of a sphere to one of the pie domes.
7. They should be quite solid now, so you should be able to easily flip one over onto the other to make your whole pi-cake. Magic.
8. Add a very thin layer of frosting to your pi-cake now (crumb coat). Put the whole thing back into the freezer, or if there isn't enough room, the refrigerator is fine. Let set for an hour.

Step 8: Decorate and Eat

Picture of Decorate and Eat

Now you can add a nice, thick layer of frosting to the whole pi-cake. 

Add dimensions and formulas to the outside of the cylinder.

When you're done decorating, you can slide out the pieces of wax paper.

When you cut a piece out of the pi-cake, you'll see the cylinder of white cake filled with a sphere of French silk pie.

Eat voraciously, as my boyfriend is doing in this picture I caught of him.

Comments

ThatKnottyguy (author)2012-07-17

Love the cake, but at first, I thought it said said circumsizing?

cbutterball (author)2011-03-21

AMAZING. This pi cake truly captures the magical relationship between a sphere and its circumscribing cylinder. Archimedes would be proud (and full).

jackson907 (author)cbutterball2011-03-21

Aww, thanks! I worked really hard on this. The end result wasn't as structurally sound as I would have liked, but I really cared about what it meant!

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