A solid of sphere of radius 'r' is melted and recast into the shape of a solid cone of height 'r,'. find the radius of cone

Question

Mathematics

Kaylie

4 April, 11:25

A solid of sphere of radius 'r' is melted and recast into the shape of a solid cone of height 'r,'. find the radius of cone

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Answers (1)

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Con · Answer 1

Vol of sphere = 4/3πr³

let the radius of cone be x.

vol of cone = 1/3πx²h

when h=r, = 1/3πrx²

since they have the same volume,

4/3πr³=1/3πrx²

4πr³=πrx²

x²=4r²

x=2r (radius)