The plane intersects the ball, the diameter of the points at one of the points of the intersection line makes an angle
| September 19, 2021 | education
The plane intersects the ball, the diameter of the points at one of the points of the intersection line makes an angle of 45 with the plane, find the cross-sectional area if the diameter of the ball is 4√3 cm.
The OO1C triangle is rectangular and isosceles, since the OO1 angle is 45.
OS = AB / 2 = 4 * √3 / 2 = 2 * √3 cm, then 2 * CO12 = OS ^ 2.
CO1 ^ 2 = OC ^ 2/2 = 12/2 = 6.
CO1 = √6 cm.
Then Ssec = π * СО1 ^ 2 = 6 * π cm2.
Answer: The cross-sectional area is 6 * π cm2.
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