Mensuration-18

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A sphere of radius 8 cm is melted and recast into a right circular cone of height
32 cm. Find the radius of the base of the cone.

Solution: Radius of the sphere = 8 cm

Volume of the sphere = 4/3 x π R3

= 4/3 x π x 83 cu. cm

Let the radius of the cone be r cm

Volume of the cone = 1/3 x π r2 x h

i.e. 1/3 x π x r2 x 32 = 32/3 π r2 cu. cm

According to the problem

32/3 π r2 = 4/3 π R3

32/3 π r2 = 4/3 x π x 8 x 8 x 8

r2 = 4/3 x π x 8 x 8 x 8 x 3 / (32 x π)

= 8 x 8

r = 8

Therefore, the radius of the base of the cone = 8 cm

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