Find the area of the base of the cone, the height of which is 12 cm, and the generatrix is 13 cm.

A cone is a geometric body formed as a result of rotation of a right-angled triangle around one of the legs.

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.

In order to find the radius of the base, consider a triangle formed by the axial section of a cone. The height of the generatrix and the radius of the cone make up a right-angled triangle, in which the generatrix is ​​the hypotenuse, and the height and radius are the legs.

Thus:

L ^ 2 = h ^ 2 + r ^ 2;

r ^ 2 = L ^ 2 – h ^ 2;

r ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25;

r = √25 = 5 cm.

Sosn. = 52 * π = 25π = 25 * 3.14 = 78.5 cm2.

Answer: The area of ​​the base of the cone is 78.5 cm2.