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Question

A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres ?


Solution

Given radius of cylinder =6cm,

 radius of each sphere =1.5cm
raise in the level of oil=2cm

Volume of the raised oil in the cylinder = πr2h=π×62×2=72π cm3


Volume of 1 sphere

=43πr3

=43π(1.5)3=9π2cm3


Let the number of sphere which when immersed in the oil raise the level by 2cm be n. 


Then,   

Volume of n spheres = =n×9π2cm3 =Volume of the raised oil

=>n×9π2=72π

=>n=72×29=16


Hence  the required number of  spheres=16
 

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