Q45 of 56 Page 13

The radii of internal and external surface of a hollow spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder. (CBSE 2012)

We have,


The internal base radius of spherical shell, r1 = 3 cm,


The external base radius of spherical shell, r2 = 5 cm and


The base radius of solid cylinder, r = 7 cm


Let the height of the cylinder be h


As,


The hollow spherical shell is melted into a solid cylinder;


So,


Volume of solid cylinder = Volume of spherical shell


⇒ πr2h =


⇒ πr2h =


⇒ r2h =


⇒ 49 × h = (125−27)


⇒ h = × 9849


Therefore,


h =


So, the height of the cylinder is .

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