The volume of the cone is 100 pi cm³, its height is 12 cm. Calculate the area of the lateral surface of the cone.

The volume of the cone is equal to one third of the product of the area of its base by the height. Knowing the height and volume, we find the radius of the base:

V = nr ^ 2 * h / 3;

r ^ 2 = 3 * V / n * h = 3 * 100 * n / n * 12 = 300/12 = 25;

r = √25 = 5 cm.

From a right-angled triangle formed by the height of the cone, the radius of its base and the generator, according to the Pythagorean theorem, we find the generator:

r ^ 2 + h ^ 2 = l ^ 2;

l ^ 2 = 5 ^ 2 + 12 ^ 2 = 25 + 144 = 169 = 132;

l = 13 cm.

The area of the lateral surface of the cone is determined by the formula:

Side = n * r * l = n * 5 * 13 = 65p ≈ 204.2 cm2.