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Question
A copper sphere of radius 3cm is melted and recast into a right circular cone of height 3cm.find radius of base of cone?
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`
r2 = 36cm
r = 6cm
∴ Radius of base of cone(r) = 6cm
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