The generatrix of the cone 8 is inclined to the base plane at an angle of 60 °. find the area of the base of the cone.
| June 19, 2021 | education
Since the base of the cone is a circle, its area is: S = π * r², where r is the radius of the circle.
Therefore, to find the area of the base of a cone, we need to find its radius.
The generatrix of the cone is the hypotenuse of a right-angled triangle, the legs of which are the height of the cone and the radius of its base.
Thus, the radius of the base will be equal to:
r = 8 * cos 60 ° = 8 * 1/2 = 4.
The area of the base will be: S = π * 4² = 16 * π = 50.3.
Answer: S = 16 * π = 50.3.
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