Question

A solid solution of a sphere is melted of a radius 'r' is recast into the shape of solid cone of height 'r' . Then what is the radius of the base of cone?

Answer 1

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Answer 2

The Radius of the base of the cone is 2r.

Step-by-step explanation:

Given :  

A solid sphere of radius =  r  

solid cone of height,h =  r

Let the radius of the cone be ‘R’  

Volume of sphere =  Volume of cone

[Sphere is melted and recast in the shape of cone]

4/3 πr³ =  ⅓ πR²h

4r³ = R²(r)

4r³/r = R²

4r² = R²

R = √(4r²)

R = 2r

Radius of the cone = 2r

Hence, the Radius of the cone is 2r.