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.

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Use the area of a spherical cap,
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SA=2pi%2AR%2Ah
The total surface area of the sphere would occur when h=2R when,
SA%5Btot%5D=4pi%2AR%5E2
We only want 3%2F%283%2B7%29=3%2F10 of the total area so,
2pi%2AR%2Ah=%283%2F10%294pi%2AR%5E2
2h=%283%2F10%294R
h=%283%2F5%29R
h=%283%2F5%29%2810%29
h=6cm
So the value we're looking for is actually the distance from the center which would be R-h
R-h=10-6
R-h=4cm