The generatrix of the cone is 5 cm, the height is 4 cm. Find its surface area

Consider a right-angled triangle in which the generatrix of the cone is the hypotenuse, the height and radius of the base are the legs. By the Pythagorean theorem, we find the radius of the base:

r ^ 2 = l ^ 2 – h ^ 2 = 5 ^ 2 – 4 ^ 2 = 25 – 16 = 9 = 32;

r = 3 cm – base radius.

The surface area of the cone is equal to the sum of the areas of its lateral surface and the base:

S full = S side + S main.

Sbn = πr ^ 2 = 9p cm2.

The area of the lateral surface of the cone is equal to half of the product of the circumference by the generator:

Side = 0.5 * 2pr * l = prl = n * 3 * 5 = 15p cm2.

S total = 15p + 9p = 24p ≈ 75.4 cm2.