Question

The ratio between the radius of the base and the height of a cylinder is 2:3. If its 1617$c{m}^3$then its total surface area is

$\left(a\right)308c{m}^2\left(b\right)462c{m}^2\left(c\right)540c{m}^2\left(d\right)770c{m}^2$

Answer 1

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.