The radius of the ball is 8 / √ п. Through the end of the radius at an angle of 60 to it, a plane is drawn
| March 28, 2021 | education
The radius of the ball is 8 / √ п. Through the end of the radius at an angle of 60 to it, a plane is drawn find the cross-sectional area.
Let us denote by a the angle of inclination of the secant area. The cross section of the ball is a circle of radius r:
r = R * cos (a), where R is the radius of the ball.
In this case, we get:
r = 8 / √π * cos (60) = 8 / √π * √3 / 2 = 4√3 / π.
The area of the circle is determined by the formula:
S = π * r ^ 2/2 = 1/2 * π * (4√3 / π) = 1/2 * 16/3 = 8/3.
Answer: the required cross-sectional area will be 8/3.
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