SOLUTION: 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

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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)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2A8%5E2
A = 201.062 sq/ft
Find the overall area. r = (w+8)
A = pi%2A%28w%2B8%29%5E2
A = pi%28w%5E2+%2B+16w+%2B+64%29
Overall area - pool area = border area
pi%28w%5E2%2B16w%2B64%29+-+201.62
The volume of the border area = 27 cu/ft
4" = 1/3 ft
%281%2F3%29%28pi%28w%5E2%2B16w%2B64%29%29+-+201.62%29 = 27
multiply both sides by 3
pi%28w%5E2%2B16w%2B64%29+-+201.62+=+81
pi%28w%5E2%2B16w%2B64%29+=+81+%2B+201.62
pi%28w%5E2%2B16w%2B64%29+=+282.62
divide both sides by pi
w%5E2+%2B+16w+%2B+64+=+89.78
w%5E2+%2B+16w+%2B+64+-+89.78+=+0
w%5E2+%2B+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
%28pi%2A9.175%5E2%29%2F3 - 201.62%2F3 =
94.0128 - 67.021 = 26.99 ~ 27 cu/ft which is 1 cubic yd