Q12 of 227 Page 897

A spherical shell of lead whose external and internal diameter are respectively 24 cm and 18 cm, is melted and recast into a right circular cylinder 37 cm high. Find the diameter of the base of the cylinder.

External diameter of shell = 24cm and


Internal diameter of shell = 18cm


So,


External radius of shell = 12 cm and


Internal radius = 9 cm


Volume of lead in the shell = π[123–93]cm3


Let the radius of the cylinder be r cm


Height of the cylinder = 37 cm


Volume of the cylinder = πr2h = πr2(37)


π[123–93] = πr2 × 37


π × 999 = πr2 × 37


r2 = × π × 999 × π = 36cm2


r = = 6cm


Hence, diameter of the base of the cylinder = 12 cm


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