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 1199078: 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 pi. Express your solution rounded to two decimal places. (1 cubic yard = 27 cubic feet)
I don't know how to do this problem. I simply followed a sample found on this website.
Let d = depth of the border
Let w = width of border to be found
Let V = volume of pool
Let r = radius of pool
V = d•pi(w + r)^2 - pi (25•d) = 27
V = 3•pi(w + 5)^2 - pi(25•3) = 27
V = 3•pi(w + 5)^2 - 75•pi = 27
Subtract 27 on both sides.
Set V = 0 and solve for w.
0 = 3•pi(w + 5)^2 - 75•pi - 27
After solving for w, I get two approximations:
-10.27871 and 0.278711
Of course, I must reject the negative value for w because distance must be positive.
The book's answer for the width of the border is 2.71 feet wide.
What am I doing wrong?
Thank you.
Found 2 solutions by ikleyn, htmentor:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
Your error is that you use wrong value for the thickness " d " of the circular walkway.
According to the problem, it is 3 inches (sic !), which is 0.25 of the foot.
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1 foot = 12 inches
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So the correct value for d is d = 0.25 ft; NOT d = 3 ft.
They caught you in the trap, using different measurement units . . .
Happy calculations and re-calculations ( ! )
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
It looks like the only place you went wrong was you did not convert the depth in inches to feet. You should have d = 3/12 = 1/4 ft. You are mixing units in your equations. Repeat with d = 1/4 and you should get the right answer.
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