SOLUTION: a circular pool measure 14 feet across. one cubic yard 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 257304: a circular pool measure 14 feet across. one cubic yard 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 would will the border be Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a circular pool measure 14 feet across. one cubic yard 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 would will the border be
:
Change 1 cu yd to cu ft
3*3*3 = 27 cu/ft of concrete
Find the area covered if 3" thick: 3" = 3/12 = .25 ft = 108 sq/ft
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Let x = width of the concrete border
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Pool radius = 7 ft (measures 14' across)
:
Overall area - pool area = 108 sq/ft - = 108
: - (153.938) = 108
: = 108 + 153.938
: = 261.938
Divide both sides by Pi
x^2 + 14x + 49 = 83.377
:
x^2 + 14x + 49 - 83.377 = 0
:
x^2 + 14x - 34.377 = 0
Solve this using the quadratic formula
In this problem a=1; b=14; c=-34.377
:
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Positive solution is what we want here
x =
x = 2.13 ft, the width of the concrete border (2' 1.6")
:
:
Check this solution on a calc, enter
(pi*9.13^2) - (pi*7^2) = 107.9 ~ 108 sq/ft
:
108 * .25 = 27 cu.ft which is 1 cu yd
