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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.)

Thanks!

 Apr 26, 2020
 #1
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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.

 Apr 26, 2020
 #2
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Hey Rudram592, I know this is a question from AOPS...please refrain from posting them here.

 Apr 27, 2020
 #3
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Yes, your'e taking the geometry course on AoPs.

 

By the way, all AoPs problems have dollar signs next to each expression or phrase

 Apr 27, 2020

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