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# Volume and Density

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A hollow steel shaft 12 feet long has an outside diameter of 16in. The inside diameter is 9 inches. What is the weight of this shaft if the steel weighs 0.29 lbs per cubic inch?

https://brainmass.com/math/geometry-and-topology/inner-outer-diameter-cyclindrical-shaft-35576

## SOLUTION This solution is FREE courtesy of BrainMass!

Let the length of the shaft be L and its outside and inside diameters are D and d respectively.

The volume of a cylinder is given by
= pie x (diameter/2)^2 x L
= pie x (diameter^2)/4 x L

Hence the volume of the steel used is given by
volume of the outer cylinder - volume of the inner cylinder
= [pie x (D^2)/4 x L] - [pie x (d^2)/4 x L]
= pie x L x (D^2 - d^2)/4
= 3.14 x (12 x12") x (256 - 81)/4 cubic inch
= 19782 cubic inch

Now the weight per cubic inch is 0.29 lbs, weight of the shaft is

0.29 x 19782 = 5736.78 lbs.

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