How many cubic inches does this rectangular pyramid contain? Round answer to the nearest whole number.

(1 point)
Responses

1,008 in.3
1,008 in. cubed

389 in.3
389 in. cubed

1,167 in.
1,167 in. cubed

336 in.3

Width: 14 in

Height: 12 in

Length: 6 in

Triangular edge: 13.89

1 answer

To find the volume of a rectangular pyramid, you can use the formula:

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

The base area of a rectangle is calculated by multiplying its length and width. Here, the length (L) is 6 in, and the width (W) is 14 in.

  1. Calculate the base area:

\[ \text{Base Area} = L \times W = 6 , \text{in} \times 14 , \text{in} = 84 , \text{in}^2 \]

  1. Now, using the height (H) of the pyramid, which is 12 in:

\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 84 , \text{in}^2 \times 12 , \text{in} \]

  1. Calculate the volume:

\[ \text{Volume} = \frac{1}{3} \times 84 \times 12 = \frac{1}{3} \times 1008 = 336 , \text{in}^3 \]

Therefore, the volume of the rectangular pyramid is \(336 , \text{in}^3\).

The correct answer is:

336 in.³