Thread: Volume of a sphere with a cyclinder drilled through it

A ball of radius 13 has a round hole of radius 6 drilled through its center. Find the volume of the resulting solid.

This doesn't seem to be complicated, but as usual, my answers aren't correct.

Volume of the ball is (4/3)*pi*(13^3).

But what's the volume of the hole? Is the hole cylinder or spherical?

Originally Posted by thedoge

A ball of radius 13 has a round hole of radius 6 drilled through its center. Find the volume of the resulting solid.

It will not be a cylinder. Look at the top/bottom of the thing that you have drilled out. It will not be flat, it will be curved just like the ball.

First look at the circle
To me this is a slice of the ball through the center.

Now consider
If you rotate this around the y-axis you'll get the volume of the drilled hole.
So the searched volume will be