Question

Sara correctly find the volume of the square pyramid below to be 2268 ft³. What was the pyramid's height?
the lithg is the 18 and the with is 6

Answer 1

To find the height of the square pyramid given its volume, you can use the formula for the volume of a pyramid:

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

For a square pyramid, the base area is calculated as follows:

\[
\text{Base Area} = \text{side length}^2
\]

From the information provided, we have:
- Volume \( V = 2268 \text{ ft}^3 \)
- Side length of the square base \( s = 6 \text{ ft} \)

First, calculate the base area:

\[
\text{Base Area} = s^2 = 6^2 = 36 \text{ ft}^2
\]

Now, plug the base area and volume into the volume formula to solve for the height \( h \):

\[
2268 = \frac{1}{3} \times 36 \times h
\]

Multiply both sides by 3 to eliminate the fraction:

\[
3 \times 2268 = 36 \times h
\]

\[
6804 = 36h
\]

Now, divide both sides by 36 to solve for \( h \):

\[
h = \frac{6804}{36} = 189 \text{ ft}
\]

Thus, the height of the pyramid is \( 189 \text{ ft} \).