Question

A circular pool measures 10 feet across. one cubic yard of concrete is to be used to create a circular border of uniform width around the pool. if the border is to have a depth of 4 ​inches, how wide will the border​ be? (1 cubic yardequals27 cubic​ feet)

Answer 1

we know that

1 ft is equal to 12 in

1 cubic yard is equal to 27 cubic​ feet

Step 1

Find the area of the circular border of uniform width around the pool

Let

x---------> the uniform width around the pool    

we know that

The diameter of the circular pool measures 10 feet

so

the radius r=5 ft

the area of the circular border is equal to

$A=\pi *(5+x)^{2}- \pi *5^{2} \\A= \pi *[(x+5) ^{2}-5^{2} ] \\ A= \pi * [x^{2} +10x]$

step 2

volume of the concrete to be used to create a circular border is equal to

V=1 yd^{3}-------> convert to ft^{3}

V=27 ft^{3} -------> equation 1

the depth is equal to 4 in-------> convert to ft

depth=4/12=(1/3) ft

volume of the concrete to be used to create a circular border is also equal to

V=Area of the circular border*Depth

$V= \pi * [x^{2} +10x]*(1/3)$ -------> equation 2

equate equation 1 and equation 2

$27=\pi * [x^{2} +10x]*(1/3) \\ x^{2} +10x- \frac{81}{\pi }=0$

using a graph tool------> to resolve the second order equation

see the attached figure

the solution is the point

x=2.126 ft

therefore

the answer is

The uniform width around the circular pool border is 2.126 ft