Question

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

Answer 1

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

PLS MARK BRAINLIEST