Question

Nate baked 3 cakes using a circular cake pan of diameter 8 inches. He plans to make a layered cake with one cake on top of the other with frosting only in between the cakes and on top of the third cake. Katrina made 5 cakes using a circular cake pan of diameter 6 inches. She plans to make a layered cake with each cake on top of the other and frosting only in between the cakes and on top of the fifth cake. The height of frosting in both their cakes is the same.

Who requires more frosting?

Nate. He has to frost an area of 602.88 square inches, and Katrina has to frost an area of 141.3 square inches.

Katrina. She has more layers in her cake than Nate, and the radius of her set of cakes is only 1 inch less than the radius of Nate’s cakes.

Katrina. She has to frost an area of 94.2 square inches, and Nate has to frost an area of 75.36 square inches.

Nate. He has to frost an area that is 9.42 square inches greater than the area Katrina has to frost.

Answer 1

Are you asking someone to verify your results? If so...
\[Nate_{frosting}=\pi r^2 (3~layers) = \pi(8^2)(3)=603.19in^2\]\[Katrine_{frosting}=\pi r^2 (5~layers) = \pi(6^2)(3)=565.49in^2\]This is all neglecting the height of the cake since the question states that both cakes have the same height.