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

The adjoining figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is given. The height of the cylinder and the cone are each of 4 cm. Find the volume of the solid.

This is the Question Number 19, Exercise 17.4 of M.L Aggarwal.

Given common radius, r = 7 cm

Height of the cone, h = 4 cm

Height of the cylinder, H = 4 cm

Volume of the solid = Volume of the cone + Volume of the cylinder + Volume of the hemisphere

= (1/3)r

^{2}h +r^{2}H + (2/3) r^{3}= r

^{2}((h/3) + H + (2r/3))= (22/7)Ã—7

^{2}Ã—((4/3)+4+(2Ã—7)/3)= (22Ã—7Ã—((4+12+14)/3)

= 22Ã—7Ã—30/3

= 1540 cm

^{3}Hence the volume of the solid is 1540 cm

^{3}.