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?

1 answer

To find the volume of the pyramid that has the same base and height as the rectangular prism, we can use the formula for the volume of a pyramid.

The volume \( V \) of a pyramid is given by the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

The volume of the rectangular prism is given as \( 27 , \text{in}^3 \), and the volume of a rectangular prism is calculated using the formula:

\[ V = \text{Base Area} \times \text{Height} \]

Let \( \text{Base Area} = A \) and \( \text{Height} = h \). Hence, we have:

\[ A \times h = 27 \]

Now, substituting \( A \) and \( h \) into the volume formula for the pyramid:

\[ V_{\text{pyramid}} = \frac{1}{3} \times A \times h \]

Using the volume of the prism, we find:

\[ V_{\text{pyramid}} = \frac{1}{3} \times 27 = 9 , \text{in}^3 \]

Thus, the volume of the pyramid is \(\boxed{9} , \text{in}^3\).