Find the total surface area of the cone if its generatrix is 15 cm and the diameter of its base is 18 cm.

A cone is a geometric body formed by rotating a right-angled triangle around one of its legs.

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

Sp.p. = Sb.p. + S main ..

Since the base of the cone is a circle, its area is calculated using the formula for the area of ​​a circle:

Sosn. = πr ^ 2.

To calculate the area of ​​the lateral surface of the cone, we apply the formula:

Sb.p. = πrL, where:

r is the radius of the base;

L – generator;

π – number ≈ 3.14.

Since the radius of the circle is equal to half of its diameter, then:

r = D / 2;

r = 18/2 = 9 cm.

Sosn. = 3.14 * 9 ^ 2 = 3.14 * 81 = 254.34 cm2;

Sb.p. = 3.14 * 9 * 15 = 423.9 cm2;

Sp.p. = 423.9 + 254.34 = 678.24 cm2.

Answer: the total surface area of ​​the cone is 678.24 cm2.