A section is drawn through two generatrices of the cone, the angle between which is equal to (alpha).
| September 8, 2021 | education
A section is drawn through two generatrices of the cone, the angle between which is equal to (alpha). Find the area of this section if the radius of the base of the cone is R, and the generatrix is inclined to the plane of the base at an angle (Betta)
The RNS triangle is rectangular, in which, through the angle and leg, we determine the length of the SC hypotenuse.
CosOSC = R / CK.
CK = R / Cosβ.
Section CDK is an equilateral triangle, then DK = SK = R / Cosβ.
Determine the area of the triangle CDK.
Ssdk = SK * DK * Sinα / 2 = (R / Cosβ) * (R / Cosβ) * Sinα / 2 = R ^ 2 * Sinα / 2 * Cos2β.
Answer: The cross-sectional area is R2 * Sinα / 2 * Cos2β.
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