Use the image to answer the question.

An illustration shows a rectangular pyramid with a length of 14 inches, a width of 6 inches, and a perpendicular height of 12 inches. The face with the length of 6 inches has a slant height of 13.89 inches. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.

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

1,167 in.3
1,167 in. cubed

389 in.3
389 in. cubed

336 in.3

1 answer

To calculate the volume of a rectangular pyramid, we can use the formula:

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

  1. First, calculate the base area. The base of the pyramid is a rectangle with length (l) of 14 inches and width (w) of 6 inches.

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

  1. Next, we know the height (h) of the pyramid is 12 inches.

  2. Now, substitute these values into the volume formula:

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

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

\[ \text{Volume} = 336 , \text{in}^3 \]

Thus, the volume of the rectangular pyramid is:

\[ \boxed{336 , \text{in}^3} \]

The correct response is 336 in.³.