Volume of Pyramids Quick Check

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Question
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

336 in.3
336 in. cubed

389 in.3
389 in. cubed

1,167 in.3

1 answer

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

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

  1. Calculate the base area: The base of the pyramid is a rectangle with a length of 14 inches and a width of 6 inches.

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

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

  3. Calculate the volume: Now plug the values into the volume formula:

    \[ \text{Volume} = \frac{1}{3} \times 84 , \text{in}^2 \times 12 , \text{in} = \frac{1}{3} \times 1008 , \text{in}^3 = 336 , \text{in}^3 \]

Therefore, the volume of the rectangular pyramid is 336 cubic inches.

The correct response is: 336 in.³ (336 in. cubed).