Priya is making a four-layered wedding cake. Her cake is in the shape of a cylinder with a radius of 6 inches. Each layer has a height of 2 inches. What is the total surface area of Priya’s four cake layers, before stacking? Use 3.14 for π and round to the nearest hundredth.(1 point)
in.2
The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height.
For each layer of Priya's cake:
Lateral surface area = 2 * 3.14 * 6 * 2 = 75.36 in^2
Since she has 4 layers, the total surface area for all four layers before stacking would be:
Total surface area = 4 * 75.36 = 301.44 in^2
Therefore, the total surface area of Priya's four cake layers before stacking is 301.44 square inches.
no not the answer
My apologies for the mistake in the previous response. Let's correct it:
To find the total surface area of Priya's four cake layers, we need to calculate the area of each layer and then add them all up:
1. The lateral surface area of each layer:
Lateral surface area = 2 * π * 6 * 2 = 24π square inches
2. The total surface area of all four layers:
Total surface area = 4 * 24π = 96π square inches
Now, rounding to the nearest hundredth using π ≈ 3.14:
Total surface area ≈ 96 * 3.14 ≈ 301.44 square inches
Therefore, the correct total surface area of Priya's four cake layers, before stacking, is approximately 301.44 square inches.
u still gave the same answer. is there a different way to work the problem
Apologies for the confusion. Let's approach the problem differently.
Each layer of the cylindrical cake has a top and bottom circle, along with the lateral surface area.
1. The area of the top and bottom circle of each layer:
Area = π * r^2
Area = π * 6^2
Area = 36π square inches
2. The lateral surface area of each layer:
Lateral surface area = 2 * π * r * h
Lateral surface area = 2 * π * 6 * 2
Lateral surface area = 24π square inches
3. Total surface area for one layer:
Total surface area = 2 * (36π) + 24π
Total surface area = 72π + 24π
Total surface area = 96π square inches
4. Total surface area for all four layers:
Total surface area = 4 * 96π
Total surface area = 384π square inches
Using π ≈ 3.14:
Total surface area ≈ 384 * 3.14
Total surface area ≈ 1205.76 square inches
Therefore, the total surface area of Priya's four cake layers, before stacking, is approximately 1205.76 square inches.