A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone.

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Solution

The internal and external radii of the hollow sphere are 2cm and 4cm respectively. Therefore, the volume of the hollow sphere is

The hollow spherical shell is melted to recast a cone of base- radius 4cm. Let, the height of the cone is h. Therefore, the volume of the cone is

Since, the volume of the cone is same as the volume of the hollow sphere, we have

Therefore, the height of the cone is

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