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?

2 Answers
Dec 22, 2017

#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#

Dec 22, 2017

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.