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The volume of a right circular cone is 9856 cm cube and the area of its base is 616 cm square . Find (i) the slant height of the cone. (ii) total surface area of the cone.

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This is the Important question of class 10 Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD.
The volume of a right circular cone and the area of its base is given .
Find (i) the slant height of the cone. (ii) total surface area of the cone.
This is the Question Number 16, Exercise 17.2 of M.L Aggarwal.

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  1. This answer was edited.

    Given base area of the cone = 616 cm2

    πr2 = 616

    (22/7)×r2 = 616

    r2 = 616×7/22

    r2 = 196

    r = 14

    Given volume of the cone = 9856 cm3

    (1/3)πr2h = 9856

    (1/3)×(22/7)×14×h = 9856

    h = (9856×3×7)/(22×142)

    h = (9856×3×7)/(22×196)

    h = 48

    (i) Slant height, = √(h2+r2)

    = √(482+142)

    = √(2304+196)

    = √(2500

    = 50

    Hence the slant height of the cone is 50 cm.

    (ii) Total surface area of the cone = πr(l+r)

    = (22/7)×14×(50+14)

    = 22×2×64

    = 2816 cm2

    Hence the total surface area of the cone is 2816 cm2.

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