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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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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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1. Given the ratio of curved surface area and the total surface area = 1:2

Total surface area = 616 cm2

Curved surface area = 616/2 = 308 cm2

2rh = 308

rh = 308/2

= 308×7/2×22

rh = 49 …(i)

Total surface area, 2rh+2r2 = 616

308+2r2 = 616

2r2 = 616-308

2r2 = 308

r= 308/2 = 154

r= 154/ = 154×7/22 = 49

Taking square root on both sides

r = 7

Substitute r in (i)

rh = 49

7×h = 49

h = 49/7 = 7 cm

Volume of the cylinder, V = r2h

= (22/7)×72×7

= 1078 cm3

Hence the volume of the cylinder is 1078 cm3.

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