Question

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

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)