Volume of a sphere with a cylindrical hole

[dhphysics]

Hello all,

I am doing homework and have come upon this question:
A cylindrical hole is drilled all the way through the center of a sphere (as shown in the figure below). Show that the volume of the remaining solid depends only on the length L of the hole, not on the size of the sphere.
Figure:

I think the problem should be solved using cylindrical shells, but I'm not sure how I should start it. Can anyone give me a hint?

Thanks

 

[SteamKing]

Hello all,

I am doing homework and have come upon this question:
A cylindrical hole is drilled all the way through the center of a sphere (as shown in the figure below). Show that the volume of the remaining solid depends only on the length L of the hole, not on the size of the sphere.
Figure:
View attachment 88013

I think the problem should be solved using cylindrical shells, but I'm not sure how I should start it. Can anyone give me a hint?

Thanks

If this is homework, in future, please fill out the Homework template and post it in the relevant HW forum.

[Note: I've moved this thread to the Calculus HW forum for you.]

 

[BvU]

Hello dhph,

How about if you try to find the volume of such a bead by revolving the shaded area around the x-axis ? Good chance R drops out !