A ball with a radius of 12 cm is completely crossed. The cross-sectional area of the ball is 36 cm2.

A ball with a radius of 12 cm is completely crossed. The cross-sectional area of the ball is 36 cm2. Find the distance from the center of the ball to the cutting plane.

Knowing the cross-sectional area of the ball, we determine the radius of the ball cross-section.

Ssection = n * r ^ 2.

36 = n * r ^ 2.

r ^ 2 = 36 / n.

r = AB = 6 / √p cm2.

From the center of the ball, draw a segment OA, which is equal in length to the radius of the ball OA = R.

The OB segment is the distance between the centers of the ball and the circle in the section that we need to calculate.

In a right-angled triangle ОАВ, according to the Pythagorean theorem, we define the leg ОВ.

OB ^ 2 = OA ^ 2 – AB ^ 2 = 12 ^ 2 – (6 / √n) ^ 2 = 144 – 36 / n = 36 * (4 – 1 / n).

ОВ = 6 * √ (4 – 1 / p).

Answer: The distance is 6 * √ (4 – 1 / p).