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 cm
Slant height, l = 25 cm
We know that l2 = h2+r2
Height of the conical vessel, h = √(l2-r2)
= √(252-72)
= √(625-49)
= √576
= 24 cm
Volume of the cone = (1/3)r2h
=(1/3)×(22/7)×72×24
= 22×7×8
= 1232 cm3
= 1.232 litres [1 litre = 1000 cm3]
Hence the volume of the cone is 1.232 litres.
(ii) Given height, h = 12 cm
Slant height, l = 13 cm
We know that l2 = h2+r2
Radius of the conical vessel, r = √(l2-h2)
= √(132-122)
= √(169-144)
= √25
= 5 cm
Volume of the cone = (1/3)r2h
=(1/3)×(22/7)×52×12
= (22/7)×25×4
= 2200/7 cm3
= 2.2/7 litres [1 litre = 1000 cm3]
= 0.314 litres
Hence the volume of the cone is 0.314 litres.