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 1048464: 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 3 inches, how wide will the border be? Use 3.14 to approximate π. Express your solution rounded to two decimal places. (1 cubic yard = 27 cubic feet).
You can put this solution on YOUR website! 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 3 inches, how wide will the border be?
Use 3.14 to approximate π. Express your solution rounded to two decimal places. (1 cubic yard = 27 cubic feet).
:
let w = the width of the border
3 inches = .25 ft
:
Then the circular area including pool and the border, radius =(w+5)
Border area = Total area - pool area
B.A =
B.A = 3.14(w^2 +10w + 25) - (3.14*25)
B.A.= 3.14w^2 + 31.4w + 25 - 78.5
B.A.= 3.14w^2 + 31.4w - 53.5
Using the volume (27) given and thickness of this area (.25ft)
.25(3.14w^2 + 31.4w - 53.5) = 27
.785w^2 + 7.85w - 13.375 - 27 = 0
a quadratic equation
.785w^2 + 7.85w - 13.625 = 0
I got a positive solution
w = 1.51 ft wide, the concrete border
