Tom baked 2 cakes using a circular cake pan of diameter 10 inches. He plans to make a layered cake with one cake on top of the other with frosting only in between the two cakes and on top of the second cake. Maria baked 3 cakes using a circular cake pan of diameter 6 inches. She plans to make a layered cake with one cake on top of the other and frosting only in between the cakes and on top of the third cake. The height of frosting in both their cakes is the same.

Who requires more frosting?

Question

Tom baked 2 cakes using a circular cake pan of diameter 10 inches. He plans to make a layered cake with one cake on top of the other with frosting only in between the two cakes and on top of the second cake. Maria baked 3 cakes using a circular cake pan of diameter 6 inches. She plans to make a layered cake with one cake on top of the other and frosting only in between the cakes and on top of the third cake. The height of frosting in both their cakes is the same.  

Who requires more frosting?

anonymous · Answer

Is it tom?

anonymous · Answer

Let f be the height of the frosting.  Form the ratio of the frosting required for Tom's cake to that of Maria's cake.$$\frac{2 \pi  5^2f}{3\pi  3^2f}=\frac{50}{27} $$Is it tom?  Yes.

anonymous · Answer

Therefor he has to frost an area of 157 square inches, and Maria has to frost an area of 84.78 square inches.

anonymous · Answer

@RoLexx 
I formulated the answer in terms of volume, however, the f factor divides out giving area ratios.

Thank you for the medal.

anonymous · Answer

You're so very welcome but I want to thank you more

anonymous · Answer

You are welcome.