First, calculate the surface area of each cylinder layer:
Bottom layer:
Radius = 24 cm / 2 = 12 cm
Surface area = 2 * π * 12 * 8.5 + π * 12^2 = 2 * π * 102 + π * 144 = 204π + 144
Middle layer:
Radius = 21.5 cm / 2 = 10.75 cm
Surface area = 2 * π * 10.75 * 8.5 + π * 10.75^2 = 2 * π * 91.375 + π * 115.5625 = 182.75π + 115.5625
Top layer:
Radius = 19 cm / 2 = 9.5 cm
Surface area = 2 * π * 9.5 * 8.5 + π * 9.5^2 = 2 * π * 80.75 + π * 90.25 = 161.5π + 90.25
Now, add the surface areas of all three layers to find the total surface area:
Total surface area = 204π + 144 + 182.75π + 115.5625 + 161.5π + 90.25
Total surface area = 548.25π + 349.8125
Calculate the approximate value of the total surface area:
Total surface area ≈ 548.25 * 3.14159 + 349.8125
Total surface area ≈ 1723.743 + 349.8125
Total surface area ≈ 2073.5555
Therefore, the surface area of the frosted cake is approximately 2074 square centimeters.
Each layer of a three-layer cake is a cylinder with a height of 8.5 cm.
The bottom layer has a diameter of 24 cm. The middle layer has a diameter of 21.5 cm
The top layer has a diameter of 19 cm
The surface of the cake is frosted.
Calculate the surface area (to the nearest square centimeter) of the cake when it is frosted.
1 answer
1 answer