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

945 cm3
945 cm cubed

2,835 cm3
2,835 cm cubed

15 cm3
15 cm cubed

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 base, the 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:

\[
\text{base area} = 15 \, \text{cm} \times 9 \, \text{cm} = 135 \, \text{cm}^2
\]

Now, plug the base area and height into the volume formula:

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

Calculating this step by step:

1. Calculate \( 135 \times 21 \):

\[
135 \times 21 = 2835 \, \text{cm}^3
\]

2. Now divide by 3:

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

Thus, the volume of the pyramid is:

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

Therefore, the correct answer is:

**945 cm³**.