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

389 in.3
389 in. cubed

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

336 in.3
336 in. cubed
Skip to navigation

1 answer

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

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

  1. Calculate the Base Area: The base is a rectangle with a length of 14 inches and a width of 6 inches. \[ \text{Base Area} = \text{Length} \times \text{Width} = 14 , \text{inches} \times 6 , \text{inches} = 84 , \text{inches}^2 \]

  2. Use the Height: The height of the pyramid is given as 12 inches.

  3. Calculate the Volume: Now plug the base area and height into the volume formula. \[ V = \frac{1}{3} \times 84 , \text{inches}^2 \times 12 , \text{inches} \] \[ V = \frac{1}{3} \times 1008 , \text{inches}^3 \] \[ V = 336 , \text{inches}^3 \]

Now, rounding to the nearest whole number gives \( 336 , \text{inches}^3 \).

Thus, the answer is:

336 in.³