The height of the cone is 5, the radius of the base is 8. Find the generatrix of the cone.
| April 10, 2021 | education
The height of the cone, its generatrix and the radius of the base form a right-angled triangle, in which the generatrix is the hypotenuse. By the Pythagorean theorem
l² = h² + r², where l is the generatrix of the cone, h is its height, r is the radius of the base.
Or in another way:
l = √ (h² + r²).
We substitute the known values of the height and radius into this formula and find the length of the generator:
l = √ (5² + 8²) = √ (25 + 64) = √89 ≈ 9.43.
Answer: the generatrix of this cone is approximately 9.43.
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