A cylindrical drill with radius 5 is used to bore a hole through the center of a sphere of radius 8. Find the volume of the ring shaped solid that remains.
Alright, my thing is that i did not understand how to set the integral
[Math] help me to find a volume of the ring shaped solid
integration
Best Answer
If you Google on "hole through a sphere" or "napkin ring formula" you will find that the volume that remains when a sphere is pierced by a cylinder is dependent only on the height of the "ring".
In this case, the height of the remaining ring is $H$:$$H=2 \times (8^2-5^2)$$ Treat $\frac{H}{2}$ as the radius of a sphere, and the volume of the sphere is the answer.
Some time ago there was a loooong discussion in a math group about this problem: " I drill a 5" long hole centrally through a sphere. What is the volume of the remaining ring?"