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

32.67 cm3
32.67 cm cubed

32,800 cm3
32,800 cm cubed

10,933.33 cm3
10,933.33 cm cubed

98,400 cm3

1 answer

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 base area \( A \) is calculated as:

\[ A = \text{length} \times \text{width} \]

Given:

  • Length = 32 cm
  • Width = 25 cm
  • Height (altitude) = 41 cm

First, calculate the base area:

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

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

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

Now calculate:

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

Therefore, the volume of the rectangular pyramid is:

10,933.33 cm³