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

Diameter of cone=14 cm
so, Radius of cone= 7cm
      Height of cone= 8cm

      ∴ Volume of cone= 1/3*pi*r^2*h
                                  =1/3*pi*49*8 cm^3

In Sphere, External Radius R=5cm
          Let, Internal Radius = r  

    Volume of Sphere = External Volume- Internal Volume
                                  = 4/3*pi*R^3-4/3*pi*r^3
                                  =4/3*pi[R^3-r^3]
                                  =4/3*pi[5^3-r^3]

But During Conversion Volume Remains Same

     So, Volume of Sphere=Volume of Cone
            4/3*pi[125-r^3]= 1/3*pi*49*8
            4[125-r^3]=49*8
              [125-r^3]=49*2
               r^3=125-98
               r^3=27
               so, r =3 cm

           Internal Radius= 3cm
    So, Internal Diameter=3*2= 6cm
            

Answer 2

Answer:

Step-by-step explanation:

Diameter of cone=14 cm

so, Radius of cone= 7cm

      Height of cone= 8cm

      ∴ Volume of cone= 1/3*pi*r^2*h

                                  =1/3*pi*49*8 cm^3

In Sphere, External Radius R=5cm

          Let, Internal Radius = r  

    Volume of Sphere = External Volume- Internal Volume

                                  = 4/3*pi*R^3-4/3*pi*r^3

                                  =4/3*pi[R^3-r^3]

                                  =4/3*pi[5^3-r^3]

But During Conversion Volume Remains Same

     So, Volume of Sphere=Volume of Cone

            4/3*pi[125-r^3]= 1/3*pi*49*8

            4[125-r^3]=49*8

              [125-r^3]=49*2

               r^3=125-98

               r^3=27

               so, r =3 cm

           Internal Radius= 3cm

    So, Internal Diameter=3*2= 6cm