There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3 , what is the volume of the prism?

Answer 1

The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height.

Since the prism and pyramid have congruent bases, the base area of the prism is the same as the base area of the pyramid.

Let the base area be A, and the height of both the prism and pyramid be h.

Volume of the pyramid = (1/3) * base area * height
48 = (1/3) * A * h

Divide both sides by (1/3):
144 = A * h

The volume of the prism is:
V = Bh
V = Ah
V = 144 * h
V = 144h

Since we know the volume of the pyramid is 48 in.3, we can substitute A = 144 and h = 1 into the formula for the volume of the prism:

V = 144 * 1
V = 144

Therefore, the volume of the rectangular prism is 144 in.3.