You promised to bake a cake for your friend's birthday. The problem is that the only baking tray you have is 30" by 10", but the fancy plate you have been planning to present you cake on is round, with a diameter of 29". What is the best solution, if you would like to make the largest cake possible and to present it in a most elegant way?

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## 5 comments:

The area of the try is pi*r^2 = pi*(29/2)^2=660.5 sq. inches.

The baking tray (at 30x10) is 300 sq inches, which is a lot smaller -- you could fit more than two cakes on the pan if you were willing to slice them up a lot, but they wouldn't fit well at all on the pan.

I think I would just bite the bullet and bake three cakes, place them side by side (into a 30" square), cut a 29" circle out of the assembled cakes, frost it all liberally, and nibble on the leftovers!

Interesting!

Any other solutions? What can you do using one cake only?

How about this then... we cut the one cake into two 15x10s and then cut each piece into two right triangles (with 15x10 sides). Then we arrange the four pieces pinwheel fashion around the plate. We'll have to overlap a little in the middle, but we can cut off points in the center as needed.

What a beautiful solution!

I would love a cake like that.

My original intention was very simple - take a 30 x 10 cake and cut two bands of 5 x 10, leaving a 20 x 10 piece.

Then, lie one 5 x 10 band on top of this piece and one on the bottom. We get a 20 x 20 square!

This square should fit into a 29" diameter round plate. How can we make sure? The diagonal of 20 x 20 square is sqrt (20 x 20 + 20 x 20) =

sqrt (800) and is less than 29.

Am I right?

Integration by parts. The smaller you cut squares of cake, the more you can fit on the plate.

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