SOLUTION: The surface areas of two similar containers are 85 in(squared) and 42 in(squared). The volume of the smaller container is 57 in(cubed). What is the volume of the larger container?

Algebra ->  Volume -> SOLUTION: The surface areas of two similar containers are 85 in(squared) and 42 in(squared). The volume of the smaller container is 57 in(cubed). What is the volume of the larger container?       Log On


   

Question 972927: The surface areas of two similar containers are 85 in(squared) and 42 in(squared). The volume of the smaller container is 57 in(cubed). What is the volume of the larger container? Round your answer to tell nearest whole number.
Thanks!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Corresponding lengths of similar solids are in a ratio r IF and ONLY IF
corresponding surface areas are in the ratio r%5E2 ,
and volumes are in the ratio r%5E3 .

In this case, the ratio of corresponding surface areas is
r%5E2=85%2F42---> r=sqrt%2885%2F42%29 and
the volumes are in the ratio
red%28cross%28r%5E2%29%29r%5E3=%28sqrt%2885%2F42%29%29%5E3=%2885%2F42%29%5E%28%223+%2F+2%22%29 .
So, the larger volume is
%2857in%5E3%29%2885%2F42%29%5E%28%223+%2F+2%22%29=aboutred%28cross%28472.48in%5E3%29%29164.1in%5E3

NOTE: Corrected 31MAY2015. Thanks to the student who questioned the posting calculations.