Question #bb56d

1 Answer
Aaron C.
May 8, 2017

#1798.2548363691529046660366720454345#

Explanation:

Start by finding the scale factor. If the scale factor can be written as #x/y#, the ratio of the surface areas can be written as #x^2/y^2# and the ratio of the volumes can be written as #x^3/y^3#. Plug in our values for #x^2/y^2# #x=312 and y=1198#. Simplify this ratio to #x^2/y^2=156/599, x/y=(2sqrt(39))/(sqrt(599)#. Cube these to find #x^3/y^3=(312sqrt(39))/(599sqrt599)#. Then cross multiply. #(312sqrt(39))/(599sqrt599)=239/n#, meaning that #n=(143161sqrt(39/599))/312~=1798.2548363691529046660366720454345#.

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