Project #1429 - problem of archimedes - spheres and volume

Calculus II homework problem os archimedes

formula for the volume of a section of a given height: V= (1/3)(pi)h^2(3r - h) where h is the height of the section and r is the radius of the sphere.
A) if a plane at distance x= r - h from the center of the unit sphere cuts into two segments, one with twice the volume of the other, show that x must satisfy the equation: 3x^3 - 9x + 2 = 0

B) now use newton's method to find a solution to the problem of archimedes, accurate to 8 decimal places.

I don't know where to start! Thank you

 

Subject Mathematics
Due By (Pacific Time) 12/02/2012 09:24 pm
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