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 x \(\frac{3}{2}\)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