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Question

The radii of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of height 223 cm. Find the diameter of the cylinder.


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Solution

Internal radius of the hollow spherical shell
(r)=3cm

and external radius(R)=5cmVolume of metal used=43π(R3r3)=43×π[5333]cm3=43π[12527]=98×43πcm3Now volume of cylinder=98×43πcm3Height(h)=223=83cmRadius=volumeπh=98×4π×33×π×8cm=49=7cm
Diameter of the cylinder =7×2=14cm


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