The area of the great circle of the sphere is 20 pi cm2. Find the surface area of the ball.

The plane of the great circle intersects the center of the ball, therefore, the radius of this circle is equal to the radius of the ball itself (see figure). Let’s denote it by r:

rcircle = rball = r.

First, let’s express the radius of a circle from the formula for finding the area of a circle:

S circle = Pi * r2

from which we find that:

r = √ (S circle / Pi);

Since the radius of the ball and the radius of the circle are the same, we can substitute the resulting radius in the formula for finding the ball:

Sball = 4 * Pi * r ^ 2 = 4 * Pi * (√ (Scircle / Pi)) ^ 2 = 4 * S;

Substitute the numerical values and find the surface area of the ball:

Sball = 4 * 20 * Pi = 80 * Pi.

Answer: 80 * Pi.