A rectangular prism has a volume of 27 in³ If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
To find the volume of the rectangular pyramid, we need to use the formula for the volume of a pyramid, which is:
\(V = \frac{1}{3} \times \text{base area} \times \text{height}\)
Since the base and height of the pyramid are congruent to the prism, and the volume of the prism is 27 in³, we can assume that the base area of the pyramid is 9 in² (since the volume of the prism is \(3 \times \text{base area} \times \text{height} = 27\)).
Now, we can calculate the volume of the pyramid:
\(V = \frac{1}{3} \times 9 \times 9 = \frac{81}{3} = 27\)
Therefore, the volume of the rectangular pyramid is 27 in³.