Question

a solid sphere of radius r is melted and recast into the shape of a solid cone of height r find radius of the base of the cone

Answer 1

The volume of the sphere with radius r is; V (sphere)= 4pir^3/3 The volume of cone with radius x and height 4r is; V(cone)= pi(x)^2(4r) Since these two solids have the same volume, we write; 4pir^3/3=pi(x)^2(4r); r^2/3= x^2; x=r/sqrt(3) The radius of the base of the cone is r(sqrt(3)/3.