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.
Deepak BoraNewbie
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 = 1:2
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
r2 = 308/2 = 154
r2 = 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.