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 10,933.33 cm3 10,933.33 cm cubed 32,800 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 pyramid, the base area can be calculated as:

\[ \text{base area} = \text{length} \times \text{width} \]

Given the length \( L = 32 \) cm, width \( W = 25 \) cm, and altitude (height) \( h = 41 \) cm, we can first calculate the base area:

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

Now, substituting the values into the volume formula:

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

Calculating \( 800 \times 41 \):

\[ 800 \times 41 = 32800 , \text{cm}^3 \]

Now, calculating the volume:

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

Therefore, the volume of the rectangular pyramid is:

\[ \boxed{10,933.33 , \text{cm}^3} \]