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.