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) About Me  (Show Source):
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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%2F4ft
27%2F%281%2F4%29 = 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%2A6%5E2 = 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%2A%28w%2B6%29%5E2 = 221.097
FOIL, divide by pi
w^2 + 12w + 36 = 221.097%2Fpi
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 42%2F3in)
:
:
Check this. find the area using the overall radius: 8.3891 ft
pi%2A8.3891%5E2 = 221.095 sq/ft