The height and radius of the base of the cone are respectively equal to 4 and 3.

The height and radius of the base of the cone are respectively equal to 4 and 3. Find the area of the lateral surface of the cone.

The area of the lateral surface of the cone is determined by the formula: S = π * r * l, where r is the radius of the base, l is the generator.
According to the conditions of the problem, we know the radius of the base and the height of the cone. Find the generator of the cone:
By the Pythagorean theorem:
l ^ 2 = r ^ 2 + h ^ 2,
l ^ 2 = 4 ^ 2 + 3 ^ 2,
l ^ 2 = 25,
l = 5.
Thus, the area of the lateral surface of this cone will be: S = π * 3 * 5 = 15π.
Answer: S = 15π.