Question

The radii of the bases of two right circular solid cones of same height are r1 and r2 respectively. The cones are melted and recasted into solid sphere of radius R. Show that the height of each cone is given by : h=4R^3\r1^2+r2^2

Answer 1

let height for each cone be h. volume of new sphere=sum of volume of cones = 1/3×pi×h(r1^2+r2^2)=4/3×pi×R^3
so after solving LHS and RHS and cancelling pi and 3,we get h=4×R^3/(r1^2+r2^2)