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,
The answer is 2174cm²
To calculate the surface area of the cake when it is frosted, we need to calculate the surface area of each layer individually and then add them together.
First, we calculate the surface area of the bottom layer:
Radius of bottom layer = diameter / 2 = 24 cm / 2 = 12 cm
Surface area of bottom layer = π * (radius)^2 = π * 12^2 = π * 144 = 452.4 cm²
Next, we calculate the surface area of the middle layer:
Radius of middle layer = diameter / 2 = 21.5 cm / 2 = 10.75 cm
Surface area of middle layer = π * (radius)^2 = π * 10.75^2 = π * 115.56 ≈ 362.31 cm²
Finally, we calculate the surface area of the top layer:
Radius of top layer = diameter / 2 = 19 cm / 2 = 9.5 cm
Surface area of top layer = π * (radius)^2 = π * 9.5^2 = π * 90.25 ≈ 283.78 cm²
Now, we add the surface areas of all three layers to get the total surface area of the cake when it is frosted:
Total surface area = 452.4 cm² + 362.31 cm² + 283.78 cm² = 1098.49 cm² ≈ 1098 cm²
Therefore, the total surface area of the frosted cake is approximately 1098 cm².