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
[tex]A=\pi *(5+x)^{2}- \pi *5^{2} \\A= \pi *[(x+5) ^{2}-5^{2} ] \\ A= \pi * [x^{2} +10x][/tex]
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
[tex]V= \pi * [x^{2} +10x]*(1/3)[/tex] -------> equation 2
equate equation 1 and equation 2
[tex]27=\pi * [x^{2} +10x]*(1/3) \\ x^{2} +10x- \frac{81}{\pi }=0[/tex]
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
