Question

When baking a cake you have a choice of the following pans: a round cake that is 2 inches deep and has a 7-inch diameter, a 6 inches times 9-inch rectangular cake pan that is 2 inches deep.
Question: Excluding the bottom of the cake what is the surface area of each cake that will be covered by frosting?

Answer 1

Option A:
 a round cake that is 2 inches deep and has a 7-inch diameter:
 S.A = (pi) * (r ^ 2) + (2) * (pi) * (r) * (h)
 Where,
 R: cake radius
 h: height of the cake
 Substituting values:
 S.A = (3.14) * ((7/2) ^ 2) + (2) * (3.14) * (7/2) * (2)
 S.A = 82.425 in ^ 2

 Option B:
 a 6 inches times 9-inch rectangular cake pan that is 2 inches deep.
 In this case we must find the area of a rectangular prism excluding the bottom of the prism.
 S.A = 2 * (9 * 2) + 2 * (6 * 2) + (9 * 6)
 S.A = 114 in ^ 2