SOLUTION: A circular pool measures 16 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 dept of 6

Algebra ->  Volume -> SOLUTION: A circular pool measures 16 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 dept of 6      Log On


   

Question 265285: A circular pool measures 16 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 dept of 6 inches, how wide will the border be? (1 cubic yard = 27 cubic feet.)

Please help me answer this problem..... Thanks a bunch!
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
First convert 6 inches into 1/2 ft. Now all units are in feet.
let x feet be the uniform length of the concrete.
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we can find the area of the concrete as
pi%2A%288%2Bx%29%5E2+-+pi%2A8%5E2+=+16%2Api%2Ax+%2B+pi%2Ax%5E2
and then the volume os area of circle times height. So, we get
%281%2F2%29%2A%2816%2Api%2Ax+%2B+pi%2Ax%5E2%29+=+27
multiply by 2 to get
16%2Api%2Ax+%2B+pi%2Ax%5E2%29+=+54
subtract 54 to get
16%2Api%2Ax+%2B+pi%2Ax%5E2%29+-+54+=+0
by quadratic, we get x as
x ~ 1.0105 feet.