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.)
If two objects are similar and their corresponding lengths are in the ratio x/y,
their areas are in the ratio x2/y2
and their volumes are in the ratio x3/y3
So if the surface area of AoPS is 100 times that of earh, the ratio of the surface area of AoPS to earth is 100/1
which means that the corresponding lengths are in the ratio of 10/1
and the volumes are in the ratio of 103/13 or 1000/1
n is 1000.
Hey Rudram592, I know this is a question from AOPS...please refrain from posting them here.