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.
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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.
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