Question
What is the volume of a rectangular pyramid if its
5 mi. in height
7 mi. in width
and 7.5 mi. in length
5 mi. in height
7 mi. in width
and 7.5 mi. in length
Answers
GPT-4o mini
To find the volume of a rectangular pyramid, you can use the formula:
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The base of the pyramid is a rectangle, so we first calculate the area of the base:
\[
\text{Base Area} = \text{Length} \times \text{Width} = 7.5 \, \text{mi} \times 7 \, \text{mi} = 52.5 \, \text{mi}^2
\]
Now, using the height of the pyramid (5 mi), we can calculate the volume:
\[
\text{Volume} = \frac{1}{3} \times 52.5 \, \text{mi}^2 \times 5 \, \text{mi}
\]
Calculating the volume:
\[
\text{Volume} = \frac{1}{3} \times 52.5 \times 5 = \frac{262.5}{3} = 87.5 \, \text{mi}^3
\]
Thus, the volume of the rectangular pyramid is \( 87.5 \, \text{mi}^3 \).
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The base of the pyramid is a rectangle, so we first calculate the area of the base:
\[
\text{Base Area} = \text{Length} \times \text{Width} = 7.5 \, \text{mi} \times 7 \, \text{mi} = 52.5 \, \text{mi}^2
\]
Now, using the height of the pyramid (5 mi), we can calculate the volume:
\[
\text{Volume} = \frac{1}{3} \times 52.5 \, \text{mi}^2 \times 5 \, \text{mi}
\]
Calculating the volume:
\[
\text{Volume} = \frac{1}{3} \times 52.5 \times 5 = \frac{262.5}{3} = 87.5 \, \text{mi}^3
\]
Thus, the volume of the rectangular pyramid is \( 87.5 \, \text{mi}^3 \).