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

1 answer

The volume of a pyramid is given by the formula V = (1/3)bh, where b is the area of the base and h is the height.

Given that the volume of the pyramid is 48 in^3, and the height of the prism and pyramid are the same, we can set up the following equation:

48 = (1/3)bh

Since the bases of the prism and pyramid are congruent, the base area of the prism is also b. Therefore, the volume of the prism is:

V = bh

Since b = 48 / (1/3)h = 48 * 3/h = 144/h

Therefore, the volume of the prism is:
V = (144/h)h
V = 144 in^3

So, the volume of the prism is 144 in^3.