Hello. I'm having trouble with the following problem.(adsbygoogle = window.adsbygoogle || []).push({});

A round hole is drilled through the center of a spherical solid of radius r. The resulting cylindrical hole has height 4 cm. What is the volume of the solid that remains?

Here's the pic that I drew, I hope it's useful:

http://img525.imageshack.us/img525/1954/sphereyv4.png [Broken]

V of sphere = 4/3 πr^3

V of cylinder = πr^2h

h = f(r)

h = 4 cm

I haven't really gotten anywhere yet, but the following should also be useful.

I originally tried to use the shells method, the area of the rectangle of which would be A(r) = 2πr * f(r) * dr. I also noticed that as dr/dt increases dh/dt decreases.

V = (4/3 πr^3) - (πr^2h) = πr^2(4/3r - 4) <--- (I'm not sure if this is useful at all but I did it anyway)

I don't really know what I should do next. Any suggestions/help is greatly appreciated!

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# Homework Help: The Classical Bead Problem (Volumes of Sphere and Cylinder)

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