Question

What is the volume of a rectangular pyramid with a length of 32 cm, a width of 25 cm, and an altitude of 41 cm?(1 point)
Responses

98,400 cm3
98,400 cm cubed

32.67 cm3
32.67 cm cubed

32,800 cm3
32,800 cm cubed

10,933.33 cm3
10,933.33 cm cubed

Answer 1

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

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

Where the Base Area is:

\[
\text{Base Area} = \text{length} \times \text{width}
\]

Given:
- Length = 32 cm
- Width = 25 cm
- Height (altitude) = 41 cm

First, we calculate the Base Area:

\[
\text{Base Area} = 32 \, \text{cm} \times 25 \, \text{cm} = 800 \, \text{cm}^2
\]

Now we can calculate the volume:

\[
V = \frac{1}{3} \times 800 \, \text{cm}^2 \times 41 \, \text{cm}
\]

Calculating:

\[
V = \frac{1}{3} \times 800 \times 41
\]
\[
V = \frac{1}{3} \times 32800
\]
\[
V = 10933.33 \, \text{cm}^3
\]

Therefore, the volume of the rectangular pyramid is:

**10,933.33 cm³**

So, the correct response is **10,933.33 cm³**.