the ratio between the radius of the base and the height of the cylinder is 2 :3 find the total surface area of the cylinder if the volume is 1617 centimetre cube
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Given ratio = 2:3 and volume = 1617 cm^3.
Let the radius and height of the cylinder be 2x and 3x. ---- (1)
Given volume of cylinder = 1617 cm^3
pir^2h = 1617 cm^3
(22/7) * (2x)^2 * 3x = 1617
22/7 * 4x^2 * 3x = 1617
x = 7/2.
Substitute x = 7/x in (1), we get
radius = 2 * 7/2 = 7
height = 3 * 7/2 = 21/2.
T.S.A of the cylinder = 2pir(h+r)
= 2 * 22/7 * 7 * (21/2 + 7)
= 22 * 35
= 770 cm^2.
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