Question

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm³, then find the radius of the base of the cylinder.

Answer 1

Let the radius of the base and the height of the cylinder be r and h, respectively

We have,

r : h = 2 : 3 i.e `"r"/"h" = 2/3`

or `"h" = (3"r")/2`        .........(i)

As,

Volume of the cylinder = 12936 cm³

`=> pi"r"^2"h" = 12936`

`=> 22/7xx"r"^2xx(3"r")/2 = 12936`     [Using (i)]

`=> 33/7xx"r"^3=129336`

`=> "r"3 = 12936xx7/33`

⇒ r³ = 2744

`=> r = root(3)(2744)`

∴ r = 14 cm

o, the radius of the base of the cylinder is 14 cm.