The area of the great circle of the sphere is equal to S. At what distance from the center

The area of the great circle of the sphere is equal to S. At what distance from the center of the sphere is the cross-section whose area is equal to 3S / 4?

Let the radius of the larger circle be R, and the radius of the smaller circle r.

The ratio of the areas of the circles is equal to the ratio of the squares of their radii.

R ^ 2 / r ^ 2 = S / (3 * S / 4) = 4/3.

r ^ 2 = 3 * R ^ 2/4.

Let’s build the radius of the OC. In a right-angled triangle COO1, by the Pythagorean theorem,

OO1 ^ 2 = R ^ 2 – r ^ 2 = R ^ 2 – 3 * R ^ 2/4 = R2 / 4.

OO1 = R / 2 cm.

The area of the larger circle of the sphere is: S = π * R ^ 2.

R ^ 2 = S / π.

R = √ (S / π).

Then OO1 = √ (S / π) / 2 = √ (S / 4 * π) see.

Answer: From the center of the ball to the section √ (S / 4 * π) see.