SOLUTION: A 2 cu. ft. of copper is to be made into copper wire 1/8 in. in diameter. How many feet of copper wire is made?

Question 1018345: A 2 cu. ft. of copper is to be made into copper wire 1/8 in. in diameter. How many feet of copper wire is made?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have 2 cubic feet of copper.

1 cubic foot = 1 * 1 * 1 feet.

there are 12 inches to a foot.

1 cubic foot is therefore equal to 12 * 12 * 12 = 1728 cubic feet.

2 cubic feet are therefore equal to 3456 cubic inches.

the diameter of the copper wire is 1/8 inches.

the radius is therefore equal to 1/8 * 1/2 = 1/16 = .0625 inches.

the volume of the copper wire is equal to pi * r^2 * h.

since the volume is 3456 cubic inches, you get:

3456 = pi * r^2 * h.

since r = .0625 inches, the formula becomes:

3456 = pi * .0625^2 * h.

solve for h to get h = 3456 / pi / .0625^2 = 281620.2155 inches.

divide that by 12 to get h = 23468.35129 feet.

we can check the answer by converting the radius from inches to feet and then solving for the volume of the copper wire.

the radius of the copper wire is .0625 inches.

divide that by 12 to get the radius of the copper wire is .0052083333 feet.

the volume of the copper wire is equal to pi * r^2 * h.

this becomes equal to pi * (.0052083333)^2 * (23468.35129) which is equal to 2 cubic feet.

that's what it should be, so we can assume we did the math correctly.

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