The radius of the base of the cone is 3 meters and the height is 4 meters. Find the generatrix and the cross-sectional area.
| September 19, 2021 | education
The axial section of the cone is an isosceles triangle ABC, then the height BO of the cone is the height, bisector and median of triangle ABC. In a right-angled triangle AOB, by the Pythagorean theorem, we determine the length of the hypotenuse AB,
AB ^ 2 = AO ^ 2 + BO ^ 2 = 9 + 16 = 25.
AB = 5 m.
In triangle ABC, the base of AC is the diameter of the circle at the base of the cone. AC = 2 * R = 2 * 3 = 6 m.
Then Ssech = AC * BО / 2 = 6 * 4/2 = 12 m2.
Answer: The generatrix of the cone is 5 m, the axial section area is 12 m2.
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