Problema Solution
Circular pool is 10 feet across. One cubic yard of concrete will be used to make circular border of uniform width around pool. If border will have depth of 3 inches how wide will border be? 1 cubic yard = 27 cubic feet.
Answer provided by our tutors
let
d = 10 ft the diameter of the pool
w = the width of the border, w>0
h = 3 in the depth of the border
we will use the formula for volume of cylinder:
(d/2 + w)^2 * pi * 3 - (d/2)^2 * pi * 3 = 27
3pi((10/2 + w)^2 - (10/2)^2) = 27 divide both sides by 3pi
(5 + w)^2 - 5^2 = 9/pi
(5 + w)^2 = 9/pi + 25
pi = 3.14
(5 + w)^2 = 9/3.14 + 25
w = 0.28 ft
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the border will be 0.28 ft wide.