SOLUTION: How far from the center of the sphere of a radius 10 cm should a plane be passed so that the ratio of surface areas of the two zones is 3:7.

Question 1082189: How far from the center of the sphere of a radius 10 cm should a plane be passed so that the ratio of surface areas of the two zones is 3:7.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Use the area of a spherical cap,
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.
.

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The total surface area of the sphere would occur when when,

We only want of the total area so,

So the value we're looking for is actually the distance from the center which would be

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