The sphere at a distance of 5 cm from the center intersects the plane. Section radius 12cm.

The sphere at a distance of 5 cm from the center intersects the plane. Section radius 12cm. Find the surface area of the sphere.

Consider a right-angled triangle that is formed by:

– a segment h = 5 cm (connects the center of the sphere and the center of the circle in the section plane);

– the radius of the sphere R;

– the radius of the circle r = 12.

The R in this triangle is the hypotenuse.

Find R ^ 2:

R ^ 2 = h ^ 2 + r ^ 2 = 5 ^ 2 + 12 ^ 2 = 169 cm ^ 2.

Sphere area S:

S = 4nR ^ 2 = 4 * 3.14 * 169 cm ^ 2 = 2122.64 cm ^ 2.

Answer: 2122.64 cm ^ 2.