A right rectangular pyramid has an altitude of 35 m, a length of 26 m, and a width of 31 m. What is the volume of the pyramid in m3 ?(1 point) Responses 28,210 m3 28,210 m cubed 30.67 m3 30.67 m cubed 84,630 m3 84,630 m cubed 9,403.33 m3

1 answer

To find the volume of a right rectangular pyramid, you can use the formula:

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

First, we need to calculate the base area of the pyramid. The base is a rectangle, so we find the area by multiplying the length and the width.

\[ \text{Base Area} = \text{Length} \times \text{Width} = 26 , \text{m} \times 31 , \text{m} = 806 , \text{m}^2 \]

Next, we can use the height of the pyramid (altitude), which is 35 m, to calculate the volume.

\[ V = \frac{1}{3} \times 806 , \text{m}^2 \times 35 , \text{m} \]

Calculating this, we have:

\[ V = \frac{1}{3} \times 806 \times 35 = \frac{28,210}{3} \approx 9,403.33 , \text{m}^3 \]

Thus, the volume of the pyramid is approximately:

\[ \boxed{9,403.33 , \text{m}^3} \]