Question

While making a two layer cake, Savannah noticed that each of the layers of cake had a diameter of 8.5 inches and a height of 2 inches. After she was done baking, the cakes were allowed to cool and then she began the frosting process. Savannah frosted the top of the cake, the sides of the entire cake, and a layer of frosting between the two cake layers.

If every layer of frosting that Savannah spread on the cake was ½ inch thick, how much frosting did Savannah use?

Answer 1

To calculate how much frosting Savannah used, we need to calculate the surface area of each cake layer and the surface area of the frosting between the layers, and then add them together.

The formula for the surface area (SA) of a cylinder is:

SA = 2πr^2 + 2πrh

Where:
r = radius of the cylinder (half the diameter)
h = height of the cylinder

So, for each cake layer, the surface area is:

SA = 2π(8.5/2)^2 + 2π(8.5/2)(2)
SA = 164.93 square inches

For the frosting layer between the cake layers, the surface area is:

SA = π(8.5/2)^2
SA = 56.76 square inches

Since the frosting is 1/2 inch thick, we need to multiply the surface area by 1/2 to get the volume of frosting:

Volume of frosting = (1/2)(56.76) = 28.38 cubic inches

Therefore, Savannah used approximately 28.38 cubic inches of frosting.