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.
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.
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