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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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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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