Question

Elizabeth has baked a cake for her sister. The cake has two layers as shown in the diagram below. If a is 4 inches long, b is 3 inches long and c is 8 inches long, what is the volume of the cake?

Answer 1

To find the volume of the cake, we need to find the volume of each layer separately and then add them together.

Volume of the first layer:
The first layer is shaped like a rectangular prism with dimensions 4 inches, 3 inches, and 3 inches (b is the height because it is perpendicular to the base). The volume of a rectangular prism is found by multiplying the length, width, and height. So, the volume of the first layer is:
4 inches x 3 inches x 3 inches = 36 cubic inches

Volume of the second layer:
The second layer is shaped like a rectangular prism with dimensions 8 inches, 3 inches, and 3 inches (b is the height because it is perpendicular to the base). The volume of a rectangular prism is found by multiplying the length, width, and height. So, the volume of the second layer is:
8 inches x 3 inches x 3 inches = 72 cubic inches

Now, add the volumes of the two layers to get the total volume of the cake:
36 cubic inches + 72 cubic inches = 108 cubic inches

Therefore, the volume of the cake is 108 cubic inches.