- #1
Kryptonite-19
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Homework Statement
How would a circle on a sphere expand as a function of the sphere's radius as the sphere expands?
Homework Equations
none were provided
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.