Geometry: Spherical Shell

Spherical Shell
 Solid enclosed between two concentric spheres is called a spherical shell. If R and r are respectively the outer and inner radii of a spherical shell, then (i) Outer surface area = 4 R2 (ii)Volume of material = 4/3 (R3 - r3)
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 Example: The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height 32/3 cm. Find the radius of the base of the cylinder. Solution: Let the radius of the base of the cylinder be r cm. Then, Volume of the metallic solid cylinder of height 32/3 cm = Volume of the metal in the spherical shell x r2 x 32/3 = 4/3(53 - 33) 32/3 r2 = 4/3 (125 - 27) r2 = 3/32 x 4/3 x 98 r2 = 49/4 r = 7/2 Hence, radius of the base of the cylinder = 7/2 cm.

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