Question

A cone of height 8.4 cm and radius of 2.1 cm is melted and recast into a sphere. find the radius of the sphere

Answer 1

A cone is 8.4 cm high and the radius of its base is 2.1 cm. 

dimensions of the cone 

height(h) = 8.4cm

radius(r)= 2.1cm

we know that volume of the cone(V) = 1/3πr2h.

                                                     V=1/3*22/7*(2.1)^2*8.4
                      
                                                   V= 38.808 cubic cm.

cone is melted and recast into sphere.

so, the volume of the cone = the volume of the sphere.

we know that volume of the sphere= 4/3 π r3 ,
  V= 4/3*22/7*r3 cubic cm

so, volume of the cone = the volume of the sphere.
 the volume of the cone=38.808 cubic cm

4/3*22/7*r3 = 38.808

r3=(38.808*7*3)/4*22
   
   =9.261

r=cube root of 9.261

r=2.1cm