The height of the cone is 24 and the length of the generatrix is 51. Find the diameter of the base of the cone.
| August 18, 2021 | education
Consider a right-angled triangle ABO
Side AO = 24, this is the height of the cone.
Side AB = 51, this is the generatrix
OB is the radius of the base of the cone.
From the Pythagorean theorem for right-angled triangles, we find the length of the side OB
ОВ ^ 2 = 51 ^ 2 – 24 ^ 2 = 2601 – 576 = 2025
ОВ = √2025 = 45
This means that the diameter of the base of the cone is 45 * 2 = 90
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