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)

98,400 cm³

10,933.33 cm³

32.67 cm³

32,800 cm³

Answer 1

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

\[
V = \frac{1}{3} \times \text{length} \times \text{width} \times \text{height}
\]

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

Substituting the values into the formula:

\[
V = \frac{1}{3} \times 32 \, \text{cm} \times 25 \, \text{cm} \times 41 \, \text{cm}
\]

Now, calculate the volume step by step:

1. Calculate the area of the base:
\[
32 \, \text{cm} \times 25 \, \text{cm} = 800 \, \text{cm}^2
\]

2. Multiply the area by the height:
\[
800 \, \text{cm}^2 \times 41 \, \text{cm} = 32,800 \, \text{cm}^3
\]

3. Now divide by 3 to get the volume of the pyramid:
\[
V = \frac{32,800 \, \text{cm}^3}{3} = 10,933.33 \, \text{cm}^3
\]

Thus, the volume of the rectangular pyramid is **10,933.33 cm³**.