The diameter of the base of the cone is 32, and the length of the generatrix is 34. Find the height of the cone.
| September 4, 2021 | education
Consider a right-angled triangle consisting of the height h, the generatrix l = 34 and the radius of the circle r = d / 2 = 32/2 = 16, which connects the center of the circle and the generator.
Height h:
h ^ 2 = l ^ 2 – r ^ 2;
h = √ (l ^ 2 – r ^ 2) = √ (34 ^ 2- 16 ^ 2) = √ (1156 – 256) = √900 = 30.
Answer: 30
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