This is the Important question of class 10 Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD.

Here the ratio between the curved surface and the total surface of a cylinder is given

So, Find the volume of the cylinder, given that its total surface area is also given.

This is the Question Number 15, Exercise 17.1 of M.L Aggarwal.

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# The ratio between the curved surface and the total surface of a cylinder is 1 : 2. Find the volume of the cylinder, given that its total surface area is 616 cm2.

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Given the ratio of curved surface area and the total surface area = 1:2Total surface area = 616 cm^{2}Curved surface area = 616/2 = 308 cm^{2}2rh = 308rh = 308/2= 308×7/2×22rh = 49 …(i)Total surface area, 2rh+2r^{2}= 616308+2r^{2}= 6162r^{2}= 616-3082r^{2}= 308r^{2 }= 308/2 = 154r^{2 }= 154/ = 154×7/22 = 49Taking square root on both sidesr = 7Substitute r in (i)rh = 497×h = 49h = 49/7 = 7 cmVolume of the cylinder, V = r^{2}h= (22/7)×7^{2}×7= 1078 cm^{3}Hence the volume of the cylinder is 1078 cm^{3}.