The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of $2 \frac{2}{3}$ cm, find the diameter of the cylinder.

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Solution

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

The spherical shell is melted to recast a solid cylinder of length cm. Let the radius of the solid cylinder is r cm. Therefore, the volume of the solid cylinder is

Since, the volume of the hollow spherical shell is equal to the volume of the solid cylinder; we have

Hence, the diameter of the solid cylinder is two times its radius, which is 14 cm.

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The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 223 cm, find the diameter of the cylinder.

The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of $2 \frac{2}{3}$ cm, find the diameter of the cylinder.