The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm. find the height of the cylinder.

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Solution

The internal and external radii of the hollow spherical shell are 3cm and 5cm respectively. Therefore, the volume of the hollow spherical shell is

The hollow spherical shell is melted to recast a cylinder of radius 7cm. Let, the height of the solid cylinder is h. Therefore, the volume of the solid cylinder is

Since, the volume of the solid cylinder is same as the volume of the hollow spherical shell, we have

Therefore, the height of the solid cylinder is

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