The ratio between

Given,

Ratio of the base and the height of a cylinder is 2:3

So,

Let the radius of the base = r

And

The height of the cylinder = h

r : h = 2 : 3

That is,

r/h = 2/3

So,

h = 3r/2 – – – – – – – – – (i)

As,

Volume of the cylinder = 12936 cm³

⇒ πr²h=12936

⇒ 22/7 × r² × 3r/2=12936 [Using (i)]

⇒ 33/7 × r³=12936

⇒ r³ = 12936 × 7/33

⇒ r³ = 2744

⇒ r = 3√2744

Therefore,

r = 14 cm

So,

The radius of the base of the cylinder is 14 cm.