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

Answer 1

To calculate the volume \( V \) of a right rectangular pyramid, you can use the formula:

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

1. Calculate the base area: The base area \( A \) of a rectangle is given by:

\[ A = \text{Length} \times \text{Width} \]

Substituting the given dimensions:

\[ A = 26 , \text{m} \times 31 , \text{m} = 806 , \text{m}^2 \]

2. Use the height: The height \( h \) of the pyramid is given as 35 m.

3. Calculate the volume:

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

Calculating it step by step:

\[ V = \frac{1}{3} \times 806 \times 35 = \frac{1}{3} \times 28110 = 9370 , \text{m}^3 \]

Thus, the volume of the pyramid is:

\[ \boxed{9370 , \text{m}^3} \]