The radius of the base of the cone is 8 cm, and its generatrix is 10 cm, find:

| September 20, 2021 | education

The radius of the base of the cone is 8 cm, and its generatrix is 10 cm, find: a) the height of the cone b) the area of the axial section of the cone

The height of the cone is a leg in a right-angled triangle, where the hypotenuse is the generatrix of the cone, and the second leg is the radius of the base. Let’s use the Pythagorean theorem and find the height:
L² = H² + R² → H = √ (L² – R²) = √ (10² – 8²) = √36 = 6 (cm).
The axial section of the cone is an isosceles triangle with a base equal to the base diameter and a lateral side equal to the generatrix.
We find the area of this triangle or the axial section of the cone:
S = 1/2 * D * H = 1/2 * 2R * H = 1/2 * 16 * 6 = 48 (cm²).
Answer: the height of the cone is 6 cm, the area of the axial section is 48 cm².



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