+123 1. The surface area of planet AoPS is 100 times that of Earth, and its volume is \(n\) times that of Earth. What is \(n \) ?(Assume both planets are perfect spheres.)
2. Points \(A,B\) , and \(C\) are on a sphere whose radius is \(13\), If \(AB=BC=10\) , what is the longest possible value of \(AC?\)
I would discourage asking problems from AoPS, as it is in their ToS to not ask for third-party help.
+62 #1) Since the surface area is 100x of the Earth, the volume should be \(100^{3/2}=1000\) times of the Earth.
