The sphere, the volume of which is 36pi, is crossed by a plane passing through its center

The sphere, the volume of which is 36pi, is crossed by a plane passing through its center. Find the surface area of each of the resulting pieces.

Knowing the volume of the sphere, we determine its diameter.

Vsh. = 4 * n * R ^ 3/3.

R ^ 3 = 3 * Vsh. / 4 * n = 3 * 36 * n / 4 * n = 27.

R = 3 cm.

The section passing through the center is the diametrical section and divides the ball in half.

Let us determine the surface area of the ball.

Sпов = 4 * п * R² = 4 * п * 3² = 36 * п.

Then the surface area of the section parts are equal: S = Sпов / 2 = 36 * n / 2 = 18 * n.

Answer: The areas of the parts are equal to 18 * p.