What is the volume of a right circular cylinder whose curved surface area is 12 π cm² and the circumference of its base is 4 π cm?

12π cm³

We know that,

Curved surface area = 2πrh  

Circumference = 2πr

The volume of the cylinder = πr²h

We have,

The curved surface area of right circular cylinder = 12π cm^2. 

Circumference  = 4π cm². 

So,

= 2 × πr = 4 × π

= r = 2 cm

Curved surface area = 12 × π

=  2 × πrh = 12 × π

= 2 × 2 × h = 12

= h = 3 cm.

Now,

The volume of the cylinder =  πr²h

Volume = π × (2)² × 3 = 12π cm³