Volume A blade is cut through the center of a sphere of radius r (see figure). The height of the remaining spherical ring is h. Find the volume of the ring and show that it is independent of the radius of the sphere.
For unlimited access to Homework Help, a Homework+ subscription is required.
A spherical ring is the solid remains after drilling a hole through the center of a solid sphere. If the sphere has radius a and the ring has height h, prove the remarkable fact that the volume of the rind depends on h but not on a.
(a) A cylindrical drill with radius r1 is used to bore a hole through the center of a sphere of radius r2. Find the volume of the ring-shaped solid that remains.
(b) Express the volume in part (a) in terms of the height h of the ring. Notice that the volume depends only on h, not on r1 or r2.
solve this