Question 1059712: Ref. Question 1059604:
A coil of steel wire weighs 50 lbs., diameter 0.025 in. Steel weighs .283 lbs. / cu. in. Determine length of wire.
The wire is a regular cylinder.
Area of circle; pi * r^2.
3.1416 * 0.0125 * 0.0125 = 0.0049 sq. in.
0.0049 * 1 = 0.0049 cu. in. (volume of 1 ft.)
50 / .283 = 176.678 = 177 cu. in. (vol. of wire).
177 / 0.0049 = 36122.48 ft.
Corrected:
3.1416 * 0.0125 * 0.0125 = 0.00049 sq. in.
0.00049 * 12 = 0.00588 (vol. of 1 ft.)
50 / .283 = 176.678 = 177 cu. in. (wire vol.)
177 / 0.00588 = 30102.04 ft.
Answer given is less. Where am I incorrect again ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A coil of steel wire weighs 50 lbs., diameter 0.025 in. Steel weighs .283 lbs. / cu. in. Determine length of wire.
The wire is a regular cylinder.
the volume of a cylinder is equal to pi * r^2 * h.
you are given that the diameter is .025 inches.
since the radius is 1/2 the diameter, then the radius is .0125 inches.
steel weighs .283 pounds per cubic inch.
divide 50 pounds by .283 and you get 176.6784452 cubic inches.
multiply 176.6784452 times .283 pounds per cubic inches and you will get 50 pounds.
therefore, the volume of the cylinder is equal to 176.6784452 cubic inches.
since volume of a cylinder is equal to pi * r^2 * h, and you know that the radius is equal to .0125 inches, and you know the volume is equal to 176.6784452 cubic inches, then the formula becomes:
176.6784452= pi * (.0125)^2 * h
solve for h to get h= 176.6784452 / (pi * (.0125)^2.
you will get h = 359926.3731 inches.
if you want the answer in feet, than you have to divide by 12 to get:
h = 359926.3731 inches / 12 = 2993.86443 feet.
you shouldn't round until the very end unless they tell you what rounded number to use.
for example, you are using 3.1416 for pi.
assuming that's what they told you to do, then your answer would be:
50 pounds divided by .283 = 176.6784452.
don't round this at this time.
v = pi * r^2 * h
solve for h to get h = v / (pi * r^2)
r is in inches, not feet.
v is in cubic inches.
pi is equal to 3.1416.
formula becomes 176.6784452 / (.0125^2 * 3.1416) = 359925.5314 inches.
divide by 12 to get 29993.79428 feet.
the difference between using the unrounded version of pi rather than the rounded version of pi is not very large,but it is there.
where i think you went wrong is here.
these two statements are suspect.
3.1416 * 0.0125 * 0.0125 = 0.0049 sq. in.
0.0049 * 1 = 0.0049 cu. in. (volume of 1 ft.)
3.1416 * .0125 * .0125 is equal to .00049 square inches., not .0049 square inches.
also, .00049 * 1 = .00049 cubic inches is not the volume of 1 foot.
it is the volume of 1 inch.
note that your error of .0049 rather than .00049 was propagated into your second statement as well.
if the height of the cylinder is 1 inch, then the volume would be pi * r^2 * h which would be 3.1416 * .0125^2 * 1 which would be equal to .000490875 cubic inches.
you rounded the intermediate answer, which you should also not do.
you should only round at the end.
so you really have total cubic inches = 176.6784452 and you really had volume of 1 inch = .000490875.
this give you total inches of 176.6784452 / .000490875 = 359925.5314 inches.
convert that to fee by dividing by 12 and you get 29993.79428 feet.
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