A rectangular pyramid has a volume of 420 in.3. If a rectangular prism has a base and heigh congruent to the pyramid, what is the volume of the prism?

Answer 1

Since the volume of a rectangular pyramid is given by the formula:

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

And we know that the volume of the pyramid is 420 in.3, we can write:

\[ 420 = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

Since the base and height of the prism are congruent to the pyramid, the volume of the rectangular prism can be calculated as:

\[ \text{Volume of prism} = \text{Base Area} \times \text{Height} \]

But, because the base and height of the prism are the same as the pyramid, the volume of the prism is three times the volume of the pyramid:

\[ \text{Volume of prism} = 3 \times 420 = 1260 \text{ in.}^3 \]

Therefore, the volume of the rectangular prism is 1260 in.3.