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