A rectangular prism has a volume of 36 cubed inches. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?

Answer 1

The volume of a rectangular prism is calculated by multiplying its length, width, and height. Since the volume of the prism is 36 cubic inches, and the base and height of the prism are congruent, we can assume that all three dimensions of the prism are the same.

Let's assume the dimensions of the prism are x inches each. Therefore, x * x * x = 36. Solving for x, we get x = 3 inches.

Now, the volume of the rectangular pyramid with the same dimensions as the prism can be calculated using the formula: (1/3) * base area * height. Since the base and height of the pyramid are congruent to the prism, the base area is 3*3 = 9 square inches, and the height is 3 inches.

Therefore, the volume of the pyramid = (1/3) * 9 * 3 = 9 cubic inches.