The height of the cone is 72 and the length of the generatrix is 78, find the axial sectional area of this cone.
| February 7, 2021 | education
The height of the cone and the radius of its base make up a right-angled triangle, in which the legs are the height and radius of the base, and the hypotenuse is the generatrix of the cone.
By the condition of the problem, we know the generator and the height. Using the Pythagorean theorem, we find what the radius of the base is equal to. Let’s denote it by x.
78² = 72² + x²,
х² = 6084 – 5184,
х² = 900,
x = 30.
The axial section of the cone is a triangle, the height of which is equal to the height of the cone, and the base is equal to two radii of the base of the cone. Therefore, the cross-sectional area will be equal to:
72 * 30 = 2160.
Answer: 2160.
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