A cutting plane is drawn perpendicular to the radius of the sphere, dividing the radius in half.

A cutting plane is drawn perpendicular to the radius of the sphere, dividing the radius in half. the cross-sectional area is 75n cm ^ 2 find the radius of the ball.

The section of a sphere by a plane is a circle whose area is equal to nr2, where r is the radius of the section. Find the square of the section radius:
Ssech = nr^2;
r2 = Ssection / n = 75p / n = 75.
Consider a right-angled triangle formed by the radius of the ball R, half the radius of the ball perpendicular to the section plane, and the section radius r. By the Pythagorean theorem, we can write:
(R / 2) ^ 2 + r ^ 2 = R ^ 2;
R ^ 2/4 + r ^ 2 = R2;
R ^ 2/4 + 75 = R ^ 2;
R ^ 2 + 300 = 4 * R ^ 2;
3 * R ^ 2 = 300;
R ^ 2 = 300/3 = 100;
R = √100 = 10 cm – the required radius of the given sphere.