The problem asks to find the height of a square pyramid given its volume and the length of the base edge. The volume of the square pyramid is 252 cubic feet, and the base edge is 10 feet. The answer should be rounded to the nearest tenth of a foot.

1. Problem Description

The problem asks to find the height of a square pyramid given its volume and the length of the base edge. The volume of the square pyramid is 252 cubic feet, and the base edge is 10 feet. The answer should be rounded to the nearest tenth of a foot.

2. Solution Steps

First, we need to recall the formula for the volume of a pyramid.

$V = \frac{1}{3}Bh$

where $V$ is the volume, $B$ is the area of the base, and $h$ is the height.

Since the base is a square with edge length 10 feet, the area of the base is:

$B = (\text{base edge})^2 = 10^2 = 100$ square feet.

We are given that the volume $V = 252$ cubic feet.

Substituting the values of $V$ and $B$ into the volume formula, we get:

$252 = \frac{1}{3}(100)h$

Now, we need to solve for $h$:

$252 = \frac{100}{3}h$

$h = \frac{252 \times 3}{100}$

$h = \frac{756}{100}$

$h = 7.56$

Rounding to the nearest tenth of a foot, we get $h \approx 7.6$ feet.

3. Final Answer

The height of the pyramid is 7.6 feet.