How Many Centimeters of Wire Were Used Up? | Mu Alpha Theta Math Club Question"

[Jameson]

I don't know how many are familiar with this math club, I think it is mostly a southern thing, but here is a question which remains to stump me.

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Wire of 0.1cm is tightly wound (with no gaps in between layers) around a cylindrical pole of 3cm radius between heights of 0cm and 1cm. As a result, this part of the pole thickens, and the new radius is (4+h), where h is the height. How many centimeters of wire were used up?

(Hint: Length * Cross-sectional Area = Volume)
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Ok, here are my few thoughts.

I guess you need to find the volume and the cross-sectional area, and thus divide to find the length.

For volume, an inegral of something along of the lines of $$\pi\int_{0}^{1}(4+h)^2dh$$ might find the volume.

For cross-sectional area, perhaps (3)(4+h).

Thanks,
Jameson

 

[DoubleMike]

what do they mean by no gaps between layers? Does this mean you can treat the winding as a solid shell?

 

[Jameson]

I assume so. That's how I took it.

 

[HallsofIvy]

Okay, calculate the volume of that cylindrical shell the wire forms. You know the radius of the wire so you can find the cross sectional area of the wire. The volume of wire used, which is equal to the cross sectional area time the length of wire used, must be equal to that volume.

 

[Jameson]

Those were my thoughts... can you look at my work before I calculate a wrong answer?

I don't know if I set the problem up correctly.