Question

A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere .

Answer 1

  we have ,

in a right circular cone 

d = 14 cm , r = 14/2 =7 cm

 h = 8 cm 

  & in hollow sphere

  external diameter (d1)= 10 cm , r1 = 10/2 =5 & internal diameter(d2) = ?

  then ,

      v. of cone = v . of hollow sphere

     1/3πr2h = 4/3π(r31-r32)

   1/3 * 7*7*8 = 4/3 (53- r32)

   1*7*7*8 = 4 (125 - r32)

   49*8 =4 (125- r32)
    392/4=  (125-r32)
    98 -125 = - r32

  - 27 = - r32

  3 = r 2

  so, internal radius ( r 2 ) = 3 cm

     internal diameter ( d2) = 2*3 = 6cm

     hence , d2 = 6cm