To find the height of a pyramid with a given volume and a square base, follow these steps:
1. Identify the given values:
- Volume ([tex]\(V\)[/tex]) = 960 cubic inches
- Side length of the square base ([tex]\(s\)[/tex]) = 12 inches
2. Recall the formula for the volume of a pyramid:
[tex]\[
V = \frac{1}{3} \times \text{base area} \times \text{height}
\][/tex]
For a square base, the base area ([tex]\(A\)[/tex]) is calculated as:
[tex]\[
A = s^2
\][/tex]
3. Calculate the base area using the side length:
[tex]\[
A = 12 \, \text{inches} \times 12 \, \text{inches} = 144 \, \text{square inches}
\][/tex]
4. Rearrange the volume formula to solve for height ([tex]\(h\)[/tex]):
[tex]\[
h = \frac{3V}{A}
\][/tex]
5. Substitute the known values into the equation:
[tex]\[
h = \frac{3 \times 960 \, \text{in}^3}{144 \, \text{in}^2}
\][/tex]
6. Calculate the height:
[tex]\[
h = \frac{2880}{144} = 20 \, \text{inches}
\][/tex]
So, the height of the pyramid is [tex]\(\boxed{20}\)[/tex] inches.
