The generatrix of the 12 cm cone is inclined to the base plane at an angle of 60 degrees. Find the area of the base of the cone.
The base of the cone is a circle, and therefore it is calculated by the formula: S = pi * r2, where S is the area of the circle, pi is the number of pi, and r is the radius of the circle.
The generatrix of the cone and its radius form a right-angled triangle with an angle at the base of 60 degrees, which means that the 2nd angle is equal to: 180 – 60 – 90 = 30 degrees.
And we know that the leg of a right-angled triangle, which lies against an angle of 30 degrees, is twice less than the hypotenuse and is equal to 12/2 = 6 cm.
Now we know the radius of the circle (6 cm) and can calculate its area: S = 3.14 * 36 ~ 113 cm2.
Therefore, our answer is 113 cm2.
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