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The ratio between the radius of the base and the height jof a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm3.

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Given,

Ratio between radius and height of a cylinder = 2:3

\(\frac{r}{h}\) = \(\frac{2}{3}\)

= 3r = 2h or h \(\frac{3}{2}\)r

Volume of cylinder = 1617 cm3

= πr2h = 1617

\(\frac{22}{7}\)x r2\(\frac{3}{2}\)r = 1617

= r3\(\frac{1617\times 14}{66}\) = 343

= r = \(\sqrt{343}\) = 7 cm

Radius = 7 cm

Height = \(\frac{3}{2}\) x 7 = \(\frac{21}{2}\) cm = 10.5 cm

∴ total surface area of cylinder = 2πr(h + +r) = 2 x \(\frac{22}{7}\) x 7(7 + 10.5) = 44 x 17.5 = 770 cm2

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