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The perimeter of the base of a cone is 44 cm and the slant height is 25 cm. Find the volume and the curved surface of the cone.

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An Important Question of class 10 Based on Mensuration Chapter of M.L Aggarwal for ICSE BOARD.
Here given the perimeter of the base of a cone and the slant height .
Find the volume and the curved surface of the cone.
This is the Question Number 15, Exercise 17.2 of M.L Aggarwal.

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1 Answer

  1. This answer was edited.

    Given perimeter of the base of a cone = 44 cm

    2πr = 44

    2×22/7×r = 44

    r = 44×7/(2×22)

    r = 7 cm

    Slant height, l = 25

    height, h = √(l2-r2)

    h = √(252-72)

    h = √(625-49)

    h = √576

    h = 24 cm

    Volume of the cone, V = (1/3)πr2h

    V = (1/3)×(22/7)×72×24

    V = (22/7)×49×8

    V = 22×7×8

    V = 1232

    Hence the volume of the cone is 1232 cm3.

    Curved surface area of the cone = πrl

    (22/7)×7×25

    = 22×25

    = 550 cm2

    Hence the curved surface area of the cone is 550 cm2.

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