Question
How na y cubic inches does this rectangular pyramid contain? Round answer to nearest whole number.
Base is 14 in by 6 in. Altitude is 12 in. Edge is 13.89 in.
336 in
1,167 in
1,008 in
389 in
Base is 14 in by 6 in. Altitude is 12 in. Edge is 13.89 in.
336 in
1,167 in
1,008 in
389 in
Answers
GPT-4o mini
To calculate the volume of a rectangular pyramid, you can use the formula:
\[
V = \frac{1}{3} \cdot B \cdot h
\]
where \( B \) is the area of the base and \( h \) is the height (altitude) of the pyramid.
1. First, calculate the area of the base:
The base is a rectangle with dimensions 14 inches by 6 inches.
\[
B = 14 \cdot 6 = 84 \text{ square inches}
\]
2. Now, substitute the base area and the altitude (height) into the volume formula. The altitude \( h \) is given as 12 inches.
\[
V = \frac{1}{3} \cdot 84 \cdot 12
\]
3. Calculate the volume:
\[
V = \frac{1}{3} \cdot 84 \cdot 12 = \frac{1008}{3} = 336 \text{ cubic inches}
\]
Therefore, the volume of the rectangular pyramid is **336 cubic inches**.
So the answer from the options provided is **336 in³**.
\[
V = \frac{1}{3} \cdot B \cdot h
\]
where \( B \) is the area of the base and \( h \) is the height (altitude) of the pyramid.
1. First, calculate the area of the base:
The base is a rectangle with dimensions 14 inches by 6 inches.
\[
B = 14 \cdot 6 = 84 \text{ square inches}
\]
2. Now, substitute the base area and the altitude (height) into the volume formula. The altitude \( h \) is given as 12 inches.
\[
V = \frac{1}{3} \cdot 84 \cdot 12
\]
3. Calculate the volume:
\[
V = \frac{1}{3} \cdot 84 \cdot 12 = \frac{1008}{3} = 336 \text{ cubic inches}
\]
Therefore, the volume of the rectangular pyramid is **336 cubic inches**.
So the answer from the options provided is **336 in³**.