Question

Volume of a square pool, which has a depth of `8` feet, is `4528` cubic feet. How much fencing will be required to fence it up to a height of `3.5` feet?

Answer 1

`333.2` `feet^2` of fencing will surround the pool.

Explanation:

Since the base of the pool is a square, we can find the length of side of base by the volume formula:

Volume = Area of square `\times` Depth of pool

We know:

`\text{Area of square = (Length of side)}^2`

By putting the given values, we have:

`4528 = \text{(length of side)}^2 \times 8`

Solve for length of side,

Length of side of square base of pool = `\sqrt{4528/8}`

`=23.8` `feet`

This gives us the dimensions around the pool, which is 18.73ft for each side. Thus, each side will be `23.8 \times 3.5` `feet^2` of area, which equals `83.3` `feet^2`.

You have `4` sides to enclose the pool multiply this area by four, and you arrive at the square feet surrounding the pool:

`83.3 \times 4 = 333.2` `feet^2`

Answer 2

Fencing required to surround pool is `333.1` square feet.

Explanation:

As the volume of square pool is `4528` cubic feet

and has a depth of `8` feet

its surface area must be `4528/8=566`

and as it is in square shape its each side is `sqrt566=23.79` feet

an perimeter is `4xx23.79=95.16` feet

and fencing required to surround pool is

`95.16xx3.5=333.06~=333.1` square feet.