A rectangular prism has a volume of 27 in.3. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?

this is for connexus

1 answer

Since both the rectangular prism and the rectangular pyramid have congruent bases and heights, their volumes are proportional.

The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.

If the volume of the prism is 27 in.3, we can let l = 3 in., w = 3 in., and h = 3 in. (since 3 x 3 x 3 = 27).

The formula for the volume of a rectangular pyramid is V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.

Since the base of the pyramid is congruent to the base of the prism, the area of the base of the pyramid is also 3 x 3 = 9 in.2.

Thus, the volume of the pyramid is:

V = (1/3)(9 in.2)(3 in.)

V = 9 in.3

Therefore, the volume of the pyramid is 9 in.3.