ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10

A solid metal cylinder with given radius and height is melted down and recast into spheres of radius 3.5 cm. Calculate the number of spheres that can be made.

This is the Question Number 22, Exercise 17.5 of M.L Aggarwal.

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# A solid metal cylinder of radius 14 cm and height 21 cm is melted down and recast into spheres of radius 3.5 cm. Calculate the number of spheres that can be made.

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Given radius of the metal cylinder, r = 14 cmHeight of the metal cylinder, h = 21 cmRadius of the sphere, R = 3.5 cmVolume of the metal cylinder = r^{2}h= (22/7)Ã—14^{2}Ã—21= 22Ã—2Ã—14Ã—21= 12936 cm^{3}Volume of sphere = (4/3)R^{3}= (4/3)Ã—(22/7)Ã—3.5^{3}= 11Ã—49/3= 539/3 cm^{3}Number of spheres that can be made = Volume of the metal cylinder/ Volume of sphere= 12936 Ã·539/3= 12936 Ã—3/539= 72Hence the number of spheres that can be made is 72.