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

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

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

389 in.3
389 in. cubed

336 in.3

1 answer

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

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

In this case, the base is a rectangle with a length of 14 inches and a width of 6 inches.

  1. Calculate the base area: \[ \text{Base Area} = \text{Length} \times \text{Width} = 14 , \text{inches} \times 6 , \text{inches} = 84 , \text{square inches} \]

  2. Now, apply the formula for the volume using the given height of 12 inches: \[ \text{Volume} = \frac{1}{3} \times 84 , \text{inches}^2 \times 12 , \text{inches} \]

  3. Calculate the volume: \[ \text{Volume} = \frac{1}{3} \times 84 \times 12 = \frac{1}{3} \times 1008 = 336 , \text{cubic inches} \]

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

The correct response is:

336 in.3 336 in. cubed