# A plane is drawn in the ball perpendicular to the diameter and dividing it into parts of 6 cm and 12 cm.

**A plane is drawn in the ball perpendicular to the diameter and dividing it into parts of 6 cm and 12 cm. Find the volumes of the two resulting parts of the ball.**

Knowing the segments into which the section divides the diameter of the ball, we determine the length of this diameter.

AB = O1A + O1B = 12 + 6 = 18 cm.

Then the radius of the ball will be equal to: AB / 2 = 18/2 = 9 cm.

The volume of the smaller segment of the sphere is determined by the formula:

V1 = n * O1B ^ 2 * (AB – O1B / 3) = n * 6 ^ 2 * (9 – 6/3) = n * 36 * (9 – 2) = 252 * n cm3.

Smaller ball volume:

Vball = 4 * n * OA ^ 3/3 = 4 * n * 729 * / 3 = 972 * n cm3.

Let’s determine the volume of the larger segment:

V2 = Vball – V1 = 972 * n – 252 * n = 720 * n cm3.

Answer: The volumes of the segments are 720 * n cm3 and 252 * n cm3.