Question

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

Answer 1

To find the height of the square pyramid given its volume, we start with the formula for the volume \( V \) of a square pyramid:

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

For a square pyramid, the base area \( \text{Base Area} \) can be calculated as:

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

From your description, it seems we have dimensions of the pyramid related to its base. However, the mention of "18 and 6" is unclear. If we assume that the base has sides of length 18 ft (as the base of a square) and 6 ft (which could be the height), we can use the base dimension that is appropriate for the volume calculation.

Let's assume the base is a square of side length 18 ft.

The base area \( A \) would then be:

\[
A = 18 \times 18 = 324 \, \text{ft}^2
\]

Given that the volume \( V = 2268 \, \text{ft}^3 \), we can plug this into the volume formula to find the height \( h \):

\[
2268 = \frac{1}{3} \times 324 \times h
\]

Now, simplify and solve for \( h \):

\[
2268 = 108 \times h
\]

\[
h = \frac{2268}{108}
\]

Calculating that gives:

\[
h = 21 \, \text{ft}
\]

So, the height of the pyramid is **21 ft**.