Question

The base of a right rectangular prism and a rectangular pyramid is 4 cm^2. The height of the pyramid is 3 times larger than the prism. How does the volume of the pyramid compare to the volume of the prism?

A) The volume of the pyramid is 9 times larger than the prism. B) The volume of the pyramids is 1/3 times larger than the prism
C) The volume of both shapes are the same.
D) The volume of the pyramid is 3 times larger than the prism

Answer 1

Explanation:

D) The volume of the pyramid is 3 times larger than the prism.

The volume of a rectangular prism is given by base area * height, so the volume of the prism is 4 cm^2 * h1. The volume of a rectangular pyramid is given by base area * height / 3, so the volume of the pyramid is 4 cm^2 * (3 * h1) / 3 = 4 cm^2 * h1 * 3. Hence, the volume of the pyramid is 3 times larger than the prism.