Question

baking 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 6 inches and the radius of the pan for the top layer is 4 inches. the batter for both layers will fill the pan to a depth of 2 inches. rounded to the nearest cubic inch, darren needs blank cubic inches of batter.

Explanation:

Step1: Recall cylinder - volume formula

The volume formula for a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Calculate volume of bottom - layer

For the bottom - layer, $r$ is not given, assume the radius of the pan is the same for both layers. Let's first calculate the volume of the bottom - layer. The height of the bottom - layer $h_1 = 6$ inches.

Step3: Calculate volume of top - layer

The height of the top - layer $h_2=4$ inches.

Step4: Calculate total volume

The total height of the batter in the two pans $h = h_1 + h_2=6 + 4=10$ inches. Assume the radius of the pan $r = 2$ inches. Then the volume $V=\pi r^{2}h=\pi\times(2)^{2}\times10 = 40\pi\approx40\times3.14 = 125.6$ cubic inches. Rounding to the nearest cubic inch, the answer is 126 cubic inches.

Answer:

126 cubic inches