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

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770 cm2 Let the common multiple be x. Let the radius of the cylinder be 2x cm and its height be 3x cm. Then, volume of the cylinder = pi"r"^2"h" = $\frac{22}{7}$xx(2x)^2xx3x Therefore, $\frac{22}{7}$xx(2x)^2xx3x=1617 => $\frac{22}{7}$xx4x^2xx3x = 1617 =>$\frac{22}{7}$xx12x^3=1617 =x^3 = (1617xx7/22xx1/12) = x^3 = ($\frac{7}{2}$xx7/2xx7/2) =x^3 = ($\frac{7}{2}$)^3 => x= $\frac{7}{2}$ Now, r = 7 cm and "h" = $\frac{21}{2}$ "cm" Hence, the total surface area of the cylinder =(2pi"rh"+2pi"r"^2) `= 2pi"r"(2xx22/7xx7xx35/2)"cm"^2` = 770 cm2

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