The radius of the ball is 14 cm. A plane is drawn through the middle of the radius, perpendicular

The radius of the ball is 14 cm. A plane is drawn through the middle of the radius, perpendicular to it. Find the cross-sectional area?

Segments ОА, ОB, ОC circle radii. By condition, OH = OB / 2 = 14/2 = 7 cm.

Since the cross-sectional area is perpendicular to the radius OB, then the OCH triangle is rectangular, in which, according to the Pythagorean theorem, CH ^ 2 = OC ^ 2 – OH ^ 2 = 196 – 49 = 147.

CH = √147 = 7 * √3 cm.

Then the cross-sectional area is equal to: Ssection = π * СН ^ 2 = 147 * π cm2.

Answer: The cross-sectional area is 147 * π cm2.