SOLUTION: A circular pool measures 10 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

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Question 161919: A circular pool measures 10 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 4 inches, how wide will the border be?
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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A circular pool measures 10 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 4 inches, how wide will the border be?
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AN interesting problem
Let x = width of the concrete border ( in feet)
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Find the the area of the concrete required rather than the volume
1 cu yd = 36" * 36" * 36" = 46646 cu/inches
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Divide this by the 4" thickness and we have the area
46656%2F4 = 11664 sq/in is area of the concrete
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Change the area of the concrete to sq/ft
11664%2F144 = 81 sq/ft is the area of the concrete
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Find the area of the pool: Ap = pi%2A5%5E2 = 78.54 sq/ft
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Total area including the concrete border: 78.54 + 81 = 159.54 sq/ft
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Radius of the circular area including the border: (x+5)
pi%2A%28x%2B5%29%5E2 = 159.54
x^2 + 10x + 25 = 159.54%2Fpi
x^2 + 10x + 25 = 50.78
x^2 + 10x + 25 - 50.78
A quadratic equation
x^2 + 10x - 25.78 = 0
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Solve this using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In our equation: a=1; b=10; c=-25.78
x+=+%28-10+%2B-+sqrt%2810%5E2+-+4%2A1%2A-25.78+%29%29%2F%282%2A1%29+
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x+=+%28-10+%2B-+sqrt%28100+%2B+103.13+%29%29%2F%282%29+
Do the math here and you will find the positive answer:
x = 2.12 ft is the width of the border
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Check our solution by finding the vol of concrete
Overall area - pool area = border area
pi%2A%282.12%2B5%29%5E2 - 78.54 =
159.26 - 78.54 = 80.72 sq/ft of concrete
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Change 80.72 to sq/in: 144 * 80.72 = 11623.68 sq/inches
Find the vol by multiplying by the thickness 4"
11623.68 * 4 = 46494.72 cu/in
Change to cu yds: 46495%2F46656 = .997 cu/yds ~ 1 cu/yd