Question

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

Answer 1

To find the height of a 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, \(B\) is the area of the base, and \(h\) is the height.

Given:
- Volume \(V = 2268 \, \text{ft}^3\)
- The side length of the base (since it's a square) is \(6 \, \text{ft}\).

First, we need to calculate the area of the base \(B\):
\[
B = \text{side}^2 = 6 \, \text{ft} \times 6 \, \text{ft} = 36 \, \text{ft}^2
\]

Now we can substitute \(V\) and \(B\) into the volume formula and solve for \(h\):

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

To isolate \(h\), multiply both sides by 3:

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

\[
6804 = 36h
\]

Now, divide both sides by 36:

\[
h = \frac{6804}{36}
\]

Calculating that gives:

\[
h = 189 \, \text{ft}
\]

Therefore, the height of the pyramid is \(189\) feet.