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Suppose you have a solid sphere of radius $R$. Suppose moreover that I have a drill of radius $\frac{R}{2}$. I place the drill such that it is tangent both to the center of the sphere and its right “side”, and drill all the way through. It looks like this:

Sphere with hole drilled through it

The shape of the solid that has been removed with the drill will be cylindrical on the side tangent to the center of the sphere, but some combination of spherical and cylindrical on the side tangent to the right side of the sphere.

Question: how do I calculate the volume of the remaining solid?

I cannot think of a way to do this either geometrically or with volumes of revolution, and I don’t know how else to go about it.

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  • $\begingroup$ What exactly do you mean by tangent to the center/ right side of the sphere. $\endgroup$ – Ahmed S. Attaalla Mar 26 '17 at 21:02
  • $\begingroup$ As shown in the picture, the hole's left side is tangent to the center of the sphere, and the hole's right side is tangent to the right side of the sphere. If in doubt, the illustration is pretty clear. $\endgroup$ – hsherl Mar 27 '17 at 0:37
  • $\begingroup$ See math.stackexchange.com/questions/210420/… $\endgroup$ – cgiovanardi Mar 27 '17 at 1:18
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Often asked, standard method used.In the example given $ R=4,\, V= \frac89 R^3 $ , should be changed in this case.

Viviani Window

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