A copper sphere of radius 3cm is melted and recast into a right circular cone of height 3cm.find radius of base of cone?

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#### Solution

Given radius of sphere = 3cm

Volume of a sphere =`4/3pir^3`

`=4/3xxpixx3^3cm^3` .........(1)

Given sphere is melted and recast into a right circular cone

Given height of circular cone = 3cm.

Volume of right circular cone `=pir^2xx1/3`

`=pi/3(r)^2xx3cm^2` ..........(2)

Equating 1 and 2 we get

`4/3pixx3^3=1/3pi(r)^2xx3`

`r^2=(4/3pixx3^3)/pi`

r^{2} = 36cm

r = 6cm

∴ Radius of base of cone(r) = 6cm

Concept: Volume of a Combination of Solids

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