An Important Question of M.L Aggarwal book of class 10 Based on Mensuration Chapter for ICSE BOARD.

You have to find the capacity in litres of a conical vessel with its radius and slant height are given in this question.

This is the Question Number 06, Exercise 17.2 of M.L Aggarwal.

# Find the capacity in litres of a conical vessel with (i) radius 7 cm, slant height 25 cm (ii) height 12 cm, slant height 13 cm

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Given radius, r = 7 cmSlant height,l= 25 cmWe know thatl^{2}= h^{2}+r^{2}Height of the conical vessel, h = √(l^{2}-r^{2})= √(25^{2}-7^{2})= √(625-49)= √576= 24 cmVolume of the cone = (1/3)r^{2}h=(1/3)×(22/7)×7^{2}×24= 22×7×8= 1232 cm^{3}= 1.232 litres [1 litre = 1000 cm^{3}]Hence the volume of the cone is 1.232 litres.(ii) Given height, h = 12 cmSlant height,l= 13 cmWe know thatl^{2}= h^{2}+r^{2}Radius of the conical vessel, r = √(l^{2}-h^{2})= √(13^{2}-12^{2})= √(169-144)= √25= 5 cmVolume of the cone = (1/3)r^{2}h=(1/3)×(22/7)×5^{2}×12= (22/7)×25×4= 2200/7 cm^{3}= 2.2/7 litres [1 litre = 1000 cm^{3}]= 0.314 litresHence the volume of the cone is 0.314 litres.