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

389 in.3
389 in. cubed

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

336 in.3
336 in. cubed

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

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

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

First, we need to calculate the area of the base. The base is a rectangle with a length of 14 inches and a width of 6 inches.

\[ \text{Base Area} = \text{Length} \times \text{Width} = 14 , \text{inches} \times 6 , \text{inches} = 84 , \text{inches}^2 \]

Now, we can plug the values into the volume formula. The height of the pyramid is given as 12 inches.

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

Calculating this:

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

Thus, the volume of the rectangular pyramid is:

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