The ratio between the radius of the base and the height of a cylinder is 2:3. If its 1617cm3then its total surface area is
(a) 308 cm2 (b) 462 cm2 (c) 540 cm2 (d) 770 cm2
Let the Radius and base of the cylinder be 2x and 3x cm respectively.
Volue of cylinder = πr2h = 1617 cm3 (given)
or 22/7*(2x)2 *3x = 1617 cm3
x3 = (1617*7)/22*4*3 = 343/8
Take the cube root of both the sides.
X = 7/2 = 3.5 So Radius = 2*3.5 = 7 cm and Height = 3.5*3 = 10.5 cm.
Total Surface area of cylinder = 2πr(r+h) = 2*22/7*7(7+10.5) = 2*22*17.5 = 770 cm square.