Question

Sara correctly found the volume of the square pyramid to be 1980 ft3
. What is the height of the pyramid? Click HERE for the Formula Reference Sheet.
5
12


(1 point)
The height of the pyramid is
feet.
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Answer 1

To find the height of the square pyramid, we can use the formula for the volume of a pyramid:

\[
V = \frac{1}{3} \times B \times h
\]

Where:
- \( V \) is the volume of the pyramid,
- \( B \) is the area of the base,
- \( h \) is the height of the pyramid.

Since it's a square pyramid, the area of the base \( B \) can be expressed as:

\[
B = s^2
\]

where \( s \) is the length of one side of the square base.

The volume is given as \( 1980 \, \text{ft}^3 \). To solve for the height \( h \), we rearrange the formula:

\[
h = \frac{3V}{B}
\]

If the side length of the base \( s \) is known, we can calculate \( B \) and subsequently find \( h \). However, if you didn't provide the side length of the base, I can't calculate the height.

Assuming you refer to a side length, like \( s = 5 \) feet or \( s = 12 \) feet, we can calculate the area \( B \).

1. If \( s = 5 \, \text{ft} \):
\[
B = 5^2 = 25 \, \text{ft}^2
\]
\[
h = \frac{3 \times 1980}{25} = \frac{5940}{25} = 237.6 \, \text{ft}
\]

2. If \( s = 12 \, \text{ft} \):
\[
B = 12^2 = 144 \, \text{ft}^2
\]
\[
h = \frac{3 \times 1980}{144} = \frac{5940}{144} \approx 41.25 \, \text{ft}
\]

Please provide the side length \( s \) to get the correct height or specify the base area otherwise.