SOLUTION: 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

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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)

the width of the border is ? feet?

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
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" = ft
= 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
= 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
= 221.097
FOIL, divide by pi
w^2 + 12w + 36 =
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 4in)
:
:
Check this. find the area using the overall radius: 8.3891 ft
= 221.095 sq/ft

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