The area of the lateral surface of the cylinder is 12π cm2, and the area of its base is 4π cm2. Find the volume of a cylinder.

Knowing that the area of the base of the cylinder is 4π cm2, we can find the radius of the base:

Sop = πr ^ 2;

r2 = Sb / π = 4π / n = 4;

r = √4 = 2 cm.

Knowing the area of the lateral surface and the radius of the base, we can find the height of the cylinder:

S side = 2 * n * r * h;

h = S side / 2pr = 12p / 4p = 3 cm.

The volume of a cylinder is equal to the product of the area of the base and the height of the cylinder:

V = Sbn * h = 4p * 3 = 12p cm3.