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Question

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 1023 cm. Find the diameter of the base of the cylinder.


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Solution

Let the radius of the base of the cylinder be r cm.

Volume of the metallic solid cylinder of height 1023 cm = Volume of the metal in the spherical shell

π×r2×323=43π(5333)323r2=43(12527)r2=332×43×98r2=494r=72 cmd=72 ×2=7 cm

the diameter of the base of the cylinder = 7 cm.


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