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Circle Expansion on Expanding Sphere

by Kryptonite-19
Tags: circle, expanding, expansion, sphere
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Nov22-13, 07:05 PM
P: 5
1. The problem statement, all variables and given/known data

How would a circle on a sphere expand as a function of the sphere's radius as the sphere expands?

2. Relevant equations
none were provided

3. The attempt at a solution

[tex]\S=4\,\pi \,{R}^{2}[/tex]
[tex]A=\pi \,{r}^{2}[/tex]

[tex]{\it dA}=2\,\pi \,r{\it dr}[/tex]
[tex]{\it dS}=8\,\pi \,R{\it dR}[/tex]

[tex]{\frac {{\it dA}}{{\it dR}}}=2\,{\frac {\pi \,r{\it dr}}{{\it dR}}}[/tex]

[tex]{\frac {{\it dA}}{{\it dS}}}{\frac {{\it dS}}{{\it dR}}}={\frac {{\it dA}}{{\it dR}}}[/tex]

[tex]{\frac {{\it dr}}{{\it dR}}}=1/2\,{\frac {{\it dA}}{{\it dR}\,\pi \,r}}[/tex]

Stuck at this point.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
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