The height of the cone is 20 and the length of the generatrix is 22, find the radius of the base.
| May 31, 2021 | education
The radius of the base of the cone, its height and the generatrix are related by the ratio R ^ 2 + H ^ 2 = L ^ 2 (where R is the radius of the base, H is the height of the cone, and L is the length of the generatrix). Thus, in our case, we get the equation: R ^ 2 + 20 ^ 2 = 22 ^ 2
We solve this equation:
R ^ 2 = 22 ^ 2 – 20 ^ 2
R ^ 2 = 484 – 400
R ^ 2 = 84
R = 3√9
Answer: the radius of the base is 3√9
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