The diameter of the sphere is 50 cm.Find the length of the line of intersection

The diameter of the sphere is 50 cm.Find the length of the line of intersection of the sphere with a plane that is at a distance of 15 cm from its center

Determine the radius of the sphere. R = AO = D / 2 = 50/2 = 25 cm.

Let’s build the radius of the OC. In a right-angled triangle OO1C, according to the Pythagorean theorem:

CO1 ^ 2 = OC ^ 2 – OO1 ^ 2 = 625 – 225 = 400. CO1 = 20 cm.

Determine the circumference of the section. L = 2 * π * СО1 = 2 * 20 * π = 40 * π cm.

Answer: The length of the intersection line is 40 * π cm.