The height of the cone is 21 and the generatrix is 35. Find the diameter of the base of the cone.
| March 16, 2021 | education
A cone is a geometric body created by rotating a triangle around a leg.
The diameter of the base of the cone is a line segment connecting two points on the border of the base, passing through the center. The base diameter is equal to two of its radii:
D = 2R.
To calculate the length of the radius, we use the cone generatrix formula:
L ^ 2 = R ^ 2 + H ^ 2;
R ^ 2 = L ^ 2 – H ^ 2;
R ^ 2 = 35 ^ 2 – 21 ^ 2 = 1225 – 441 = 784;
R = √784 = 28 cm.
D = 28 2 = 56 cm.
Answer: The diameter of the base of the cone is 56 cm.
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