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.
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