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

3.8 feet

Explanation:

Answer 2

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- (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