SOLUTION: I have a hole three feet in diameter and thirty feet deep, how many cubic yards of dirt will I pull out

Question 413047: I have a hole three feet in diameter and thirty feet deep, how many cubic yards of dirt will I pull out
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the hole is 3 feet in diameter and thirty feet deep.

that's a cylinder.

volume of a cylinder is pi * r^2 * h

radius is 1.5 feet (half of the diameter).

you can convert to yards first and then get the volume or you can get the volume and then convert to yards.

it's usually easier to convert first.

since there are 3 feet to a yard, the radius is .5 yards (1.5/3 = .5)

the height is 10 yards (30/3 = 10)

the volume if pi * r^2 * h = pi * .5^2 * 10 = pi * .25 * 10 = 2.5 * pi or roughly 7.853981634 cubic yards.

if you left it in feet and converted later, you would get the following:

volume is 1.5^2 * pi * 30 feet.

volume is equal to 67.5 * pi or roughly 212.0575041 cubic feet.

to convert to cubic yards, you would have to divide by 27 (3^3 = 27).

divide by 27 and you get volume of roughly 7.853981634 cubic yards.

the answer is the same regardless of whether you converted to yards first or to cubic yards later.

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