The area of the lateral surface of the cone is 2 * √2 * Pi, the generatrix is inclined to the base plane
| April 1, 2021 | education
The area of the lateral surface of the cone is 2 * √2 * Pi, the generatrix is inclined to the base plane at an angle of 45. Find: a) the area of the cone section by a plane passing through two generatrices, the angle between which is 30. b) the radius of the base of the cone.
The area of the lateral surface of the cone is: Side = π * R * L = 2 * √2 * π.
R * L = 2 * √2.
Triangle AOB is rectangular, in which Cos45 = AO / AB = R / L = √2 / 2.
L = 2 * R / √2.
R * 2 * R / √2 = 2 * √2.
R ^ 2 = 2 * √2 * √2 / 2 = 2.
R = √2 cm.
L = 2 * √2 / √2 = 2 cm.
Let us determine the sectional area of the VCM.
Ssection = L * L * Sin30 / 2 = 4 * (1/2) / 2 = 1 cm2.
Answer: The cross-sectional area is 1 cm2, the radius is √2 cm.
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