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.
Internal radius of the hollow spherical shell
(r)=3cm
and external radius(R)=5cm∴Volume of metal used=43π(R3−r3)=43×π[53−33]cm3=43π[125−27]=98×43πcm3Now volume of cylinder=98×43πcm3Height(h)=223=83cm∴Radius=√volumeπh=√98×4π×33×π×8cm=√49=7cm
∴ Diameter of the cylinder =7×2=14cm