Question 1063495
A circular pool measures 16 feet across. One cubic yard of concrete is to be used to create a circular border with uniform width around the pool.
 The border is to have a depth of 4 inches, how wide will the border be? 
(1 cubic yard=27 cubic​ feet)
:
let w = the width of the border
:
Find the area of the pool (r = 8)
A = {{{pi*8^2}}}
A = 201.062 sq/ft
Find the overall area. r = (w+8) 
A = {{{pi*(w+8)^2}}}
A = {{{pi(w^2 + 16w + 64)}}}
Overall area - pool area = border area
{{{pi(w^2+16w+64) - 201.62}}}
The volume of the border area = 27 cu/ft
4" = 1/3 ft
{{{(1/3)(pi(w^2+16w+64)) - 201.62)}}} = 27
multiply both sides by 3
{{{pi(w^2+16w+64) - 201.62 = 81}}}
{{{pi(w^2+16w+64) = 81 + 201.62}}}
{{{pi(w^2+16w+64) = 282.62}}}
divide both sides by pi
{{{w^2 + 16w + 64 = 89.78}}}
{{{w^2 + 16w + 64 - 89.78 = 0}}}
{{{w^2 + 16w - 25.78 = 0}}}
using the quadratic formula, I got a positive of
w = 1.475 ft is the width of the border
:
:
we can check this (pool volume is 4" thick also)
overall vol - pool volume = 27 cu/ft
{{{(pi*9.175^2)/3}}} - {{{201.62/3}}} = 
94.0128 - 67.021 = 26.99 ~ 27 cu/ft which is 1 cubic yd