A rectangular prism has a base area of 25 in.² and a volume of 125 in.³. If a rectangular pyramid has a congruent base and height congruent to the prism, what is the height of the pyramid?

Answer 1

The volume of a prism can be found using the formula $V=Bh_P$ where $B$ is the base, $h_P$ is the height of the prism, and $V$ is the volume. We are given that the base area of the rectangular prism is 125 square inches and the volume is 125 cubic inches. Plugging the corresponding values in the volume formula, we get $125=25h_P$. Dividing both sides of the equation by 25, we get $h_P=5$ inches.

The volume of a pyramid can be found using the formula $V=\frac{1}{3}Bh$, where $B$ is the base, $h$ is the height of the pyramid, and $V$ is the volume. We are given that the base area of the rectangular pyramid is congruent to that of the rectangular prism, so we have $B = 25$ square inches. We are also given that the height of the rectangular pyramid is congruent to that of the rectangular prism, so $h = h_P = 5$ inches. Plugging the corresponding values in the volume formula, we get $V = \frac{1}{3}(25)(5)$. Simplifying, we get $V = \frac{1}{3}(125)$, or $V = \boxed{41.667}$ cubic inches.