Question 972927
Corresponding lengths of similar solids are in a ratio {{{r}}} IF and ONLY IF
corresponding surface areas are in the ratio {{{r^2}}} ,
and volumes are in the ratio {{{r^3}}} .
 
In this case, the ratio of corresponding surface areas is
{{{r^2=85/42}}}---> {{{r=sqrt(85/42)}}} and
the volumes are in the ratio
{{{red(cross(r^2))}}}{{{r^3=(sqrt(85/42))^3=(85/42)^("3 / 2")}}} .
So, the larger volume is
{{{(57in^3)(85/42)^("3 / 2")=about}}}{{{red(cross(472.48in^3))}}}{{{164.1in^3}}}
 
NOTE: Corrected 31MAY2015. Thanks to the student who questioned the posting calculations.