Question

Darren is baking a two-layer cake and the pan for each layer is in the shape of a cylinder. The radius of the pan for the bottom layer is 5 inches and the radius of the pan for the top layer is 3 inches. The batter for both layers will fill the pan to a depth of 2 inches. What is the volume of the cake?

Answer 1

To calculate the total volume of the cake, you need to add the volumes of both cylindrical layers. The bottom layer has a volume of 50π in³, and the top layer has a volume of 18π in³, resulting in a total volume of 68π in³.

Step-by-step explanation:

To calculate the volume of the cake that Darren is baking, we need to find the volume for each cylindrical layer and then add them up. Since both layers are cylinders and we know the radius and height for each, we can use the formula for the volume of a cylinder: V = πr²h.

For the bottom layer with a radius of 5 inches and height of 2 inches, the volume would be V1 = π(5 in)²(2 in) = π(25 in²)(2 in) = 50π in³.

For the top layer with a radius of 3 inches and also a height of 2 inches, the volume would be V2 = π(3 in)²(2 in) = π(9 in²)(2 in) = 18π in³.

Now, we just add the volumes of the bottom and top layers together to get the total volume of the cake: V_total = V1 + V2 = 50π in³ + 18π in³ = 68π in³. To get a numerical value we can multiply by π (approximately 3.14159) to find the total volume.