Question

A square prism has a volume of 2,535 cubic centimeters. A square pyramid with the same base side length as the square pyramid has a volume of 834 cubic centimeters. Which statement correctly compares the heights of the prism and pyramid?(1 point)
Responses

The height of the square prism is one-third the height of the square pyramid.
The height of the square prism is one-third the height of the square pyramid.

The height of the square prism is equal to the height of the square pyramid.
The height of the square prism is equal to the height of the square pyramid.

The height of the square prism is three times the height of the square pyramid.
The height of the square prism is three times the height of the square pyramid.

The height of the square prism is two times the height of the square pyramid.

Answer 1

Let s be the base side length, A = s^2.

h_prism = V_prism / A = 2535 / A.
h_pyramid = 3·V_pyramid / A = 3·834 / A = 2502 / A.

h_prism / h_pyramid = 2535 / 2502 = 845 / 834 ≈ 1.013.

So the prism is slightly taller than the pyramid (about 1.3% taller). None of the four given choices is exactly correct. The heights are not equal; the prism’s height is about 845/834 times the pyramid’s height.