Question

What is the volume of a rectangular pyramid with a width of 9 cm, a length of 15 cm, and an altitude of 21 cm?(1 point)
Responses

8,505 cm3
8,505 cm cubed

2,835 cm3
2,835 cm cubed

945 cm3
945 cm cubed

15 cm3

Answer 1

The volume \( V \) of a rectangular pyramid can be calculated using the formula:

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

For a rectangular pyramid, the base area \( \text{Base Area} \) is given by:

\[
\text{Base Area} = \text{Length} \times \text{Width}
\]

Given:
- Length = 15 cm
- Width = 9 cm
- Height (altitude) = 21 cm

First, calculate the base area:

\[
\text{Base Area} = 15 \, \text{cm} \times 9 \, \text{cm} = 135 \, \text{cm}^2
\]

Next, substitute the base area and height into the volume formula:

\[
V = \frac{1}{3} \times 135 \, \text{cm}^2 \times 21 \, \text{cm}
\]

Now calculate:

\[
V = \frac{1}{3} \times 2835 \, \text{cm}^3 = 945 \, \text{cm}^3
\]

Thus, the volume of the rectangular pyramid is:

\[
\boxed{945 \, \text{cm}^3}
\]