Question 1122812
A circular pool measures 12 feet across. one cubic yd 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 3 inches, how wide will the border be? 
(1 cubic yard= 27 cubic feet)
:
Find the area of the border, divide the volume by the depth; 3" = {{{1/4}}}ft
{{{27/(1/4)}}} = 108 sq/ft the area of border
:
let w = the width of the circular border
Radius of the pool is half of 12 = 6 ft, therefore
(w+6) = the radius of the circular area which includes the border
:
Find the area of the pool
{{{pi*6^2}}} = 113.097 sq/ft
Find the total area which includes the border
113.097 + 108 = 221.097 sq/ft
:
find the width of the border
{{{pi*(w+6)^2}}} = 221.097
FOIL, divide by pi
w^2 + 12w + 36 = {{{221.097/pi}}}
w^2 + 12w + 36 = 70.377
w^2 + 12w + 36 - 70.377 = 0
w^2 + 12w - 34.377 = 0
use quadratic formula, a=1; b=12; c=-34.377
the positive solution
w = 2.3891 ft is the width of the border (2 ft 4{{{2/3}}}in)
:
:
Check this. find the area using the overall radius: 8.3891 ft
{{{pi*8.3891^2}}} = 221.095 sq/ft