Question 149521
Since the ratio of the surface areas is 49:81, this means that 


{{{ratio_surface_area=49/81}}}



Now simply take the square root of the fraction to get the ratio of the sides.


{{{sqrt(49/81)=sqrt(49)/sqrt(81)=7/9}}}


So the ratio of the sides is 7:9



Now simply cube {{{7/9}}} to get the ratio of the two volumes


{{{7^3/9^3=343/729}}}


Now let x=volume of the larger cube


Since the ratio of the two volumes, this means that we can say


{{{20/x=343/729}}}



{{{20=(343/729)*x}}} Multiply both sides by x



{{{20*729=343*x}}} Multiply both sides by 729



{{{14580=343*x}}} Multiply



{{{14580/343=x}}} Divide both sides by 343




So our answer is  {{{x=14580/343}}} which is approximately {{{x=42.51}}}



So the volume of the larger cube is 42.51