The ball is crossed by a plane at a distance of 4 from the center, find the radius of the section if the radius of the ball is 5.

Points 1) the center of the ball, 2) the center of the section, 3) an arbitrary point of the sphere in the plane of the section form a right-angled triangle, in which the hypotenuse is equal to the radius of the sphere, and one of the legs is the distance from the center to the plane of the section.

The section radius is the second leg of our triangle and to calculate it we use the Pythagorean theorem:

√ (5 * 5 – 4 * 4) = √ (25 – 16) = √9 = 3.

Answer: the section radius is 3.