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 2

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Question 315664: 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 2 inches, how wide will the border be? (1 cubic yard=36 cubic feet)
Answer by ankor@dixie-net.com(22740) (Show Source):
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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 2 inches, how wide will the border be?
(1 cubic yard=36 cubic feet)
I think there is 27 cu/ft in a cubic yard, but will do the problem using 36
:
Let x = the width of the concrete border
:
From the given information we know the area of the concrete border will be:
2 in = 2/12 = ft
A = = 216 sq/ft is the area of the concrete
:
Radius of the pool = 8 ft
Radius overall, including the circular concrete border = (x+8)
:
Area of pool:
A =
A = 201 sq/ft
:
Equation for total area
= 201 + 216
:
= 417
:
x^2 + 16x + 64 =
:
x^2 + 16x + 64 = 132.74
:
x^2 + 16x + 64 - 132.74 = 0
:
x^2 + 16x - 68.74 = 0
Use the quadratic equation

In this equation, a=1, b=16, c=-68.74

:

:

Positive solution is all we want here

x =
x = 3.5 ft is the width of the concrete
:
:
Check solution by finding the total area, then subtract the pool area
r = 8 + 3.5 = 11.5
A =
A = 415.5
415.5 - 201 = 214.5 area of concrete
then
214.5 * = 35.7 ~ 36 cu/ft of concrete