The height and radius of the base of the cone are 2 cm. A secant plane is drawn through two generatrices, the angle between which is 30 °. Find the cross-sectional area.
Since, by condition, the radius of the circle at the base of the cone and the height of the cone are equal, then the right-angled triangle BOC is isosceles, ОВ = ОC = 2 cm.
Then, by the Pythagorean theorem, CB ^ 2 = OB ^ 2 + OC ^ 2 = 4 + 4 = 8.
CВ ^ 2 = √8 = 2 * √2 cm.
Then the generators CK = CM = CB = 2 * √2 cm.
The section of the CKM is an isosceles triangle with an apex angle C = 30.
Determine the cross-sectional area.
Ssection = CK * CM * Sin30 / 2 = 2 * √2 * 2 * √2 * (1/2) / 2 = 2 cm2.
Answer: The cross-sectional area is 2 cm2.
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