SOLUTION: A sphere segment has a volume of 904.78 cu.cm.If the radius of the sphere is 10cm, solve the area of the zone.

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Question 1203308: A sphere segment has a volume of 904.78 cu.cm.If the radius of the sphere is 10cm, solve the area of the zone.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


The ratio of the segment volume to the entire volume (%284%2F3%29%2Api%2Ar%5E3) is the same as the ratio of the area of the segment (S) to the entire area ( 4%2Api%2Ar%5E2):



++904.78+%2F+%28%284%2F3%29%2Api%2A10%5E3%29+ = +S+%2F+%284%2Api%2A10%5E2%29+



S = +4%2Api%2A10%5E2+%2A+%28904.78++%2F+%28%284%2F3%29%2Api%2A10%5E3%29%29+ 



S = +271.43+cm%5E2+



NOTE that I only concerned myself with the area of the spherical surface portion (i.e., the "zone" is taken to be that part of the outermost surface of the sphere), not the total area of the solid segment.