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Question

If a solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each, then n = _________.

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Solution


Radius of the solid sphere, R = 4 cm

Radius of each solid hemisphere, r = 2 cm

It is given that, the solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each.

∴ n × Volume of each solid hemisphere = Volume of the sphere

n×23πr3=43πR3

n=2×R3r3

n=2×Rr3

n=2×4 cm2 cm3 (R = 4 cm and r = 2 cm)

n=2×8

n=16

Thus, the value of n is 16.

If a solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each, then n = ___16___.

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