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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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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.

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  1. 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.

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