An Important Question of class 10 Based on Mensuration Chapter of M.L Aggarwal for ICSE BOARD.

(i)Here the sum of the radius and the height of a cylinder and the total surface area of the cylinder is given.

Find the height and the volume of the cylinder

(ii)If The total surface area of a cylinder and its height is given, then find the diameter of the base.

This is the Question Number 14, Exercise 17.1 of M.L Aggarwal.

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# (i) The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2 . Find the height and the volume of the cylinder. (ii) The total surface area of a cylinder is 352 cm2 . If its height is 10 cm, then find the diameter of the base.

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(i) Let r be the radius and h be the height of the cylinder.Given the sum of radius and height of the cylinder, r+h = 37 cmTotal surface area of the cylinder = 1628 cm^{2}2r(r+h) = 16282Ã—(22/7)Ã—rÃ—37 = 1628r = (1628Ã—7)/(2Ã—22Ã—37)r = 7 cmWe have r+h = 377+h = 37h = 37-7 = 30 cmVolume of the cylinder, V = r^{2}h= (22/7)Ã—7^{2}Ã—30= (22/7)Ã—49Ã—30= 4620 cm^{3}Hence the height and volume of the cylinder is 30 cm and 4620 cm^{3}Â respectively.(ii) Total surface area of the cylinder = 353 cm^{2}Height, h = 10 cm2r(r+h) = 3522Ã—(22/7)Ã—rÃ—(r+10) = 352r^{2}+10r = (352Ã—7)/2Ã—22r^{2}+10r = 56r^{2}+10r-56 = 0(r+14)(r-4) = 0r+14 = 0 or r-4 = 0r = -14 or r = 4Radius cannot be negative. So r = 4.Diameter = 2Ã—r = 2Ã—4 = 8 cm.Hence the diameter of the base is 8 cm.