Calculate the area of the lateral and total surfaces of the cone, the height of which is 8cm, and the radius is 6cm.

The height of the CO cone is perpendicular to the base plane and passes through the center of the circle.

Then triangle ABC is rectangular and AO = R = 6 cm.

By the Pythagorean theorem, we determine the length of the hypotenuse AC, which is the generator of the cone.

AC ^ 2 = AO ^ 2 + CO ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 + 64 = 100.

AC = 10 cm.

Determine the area of the base of the cone.

Sb = n * R2 = n * 36 cm2.

Let us determine the area of the lateral surface of the cone.

Side = n * R * L = n * R * AC = n * 6 * 10 = 60 * n cm2.

Then Scon = Sbn + Sbok = n * 36 + n * 60 = 96 * n cm2.

Answer: The area of the lateral surface is equal to n * 60 cm2, the total surface is 96 * n cm2.