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

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

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Answer 2

Answer:

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