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

2,835 cm3
2,835 cm cubed

945 cm3
945 cm cubed

15 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 \( \text{Base Area} \) 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:

\[ \text{Base Area} = 15 , \text{cm} \times 9 , \text{cm} = 135 , \text{cm}^2 \]

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

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

Now calculate:

\[ V = \frac{1}{3} \times 2835 , \text{cm}^3 = 945 , \text{cm}^3 \]

Thus, the volume of the rectangular pyramid is:

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