Similar solids volume

This one is a little tricky  !!

Since  surface area is in square units...we need to take the square root of the ratio of surface area of A  to the surface area of B to get the scale factor

The scale factor from A : B   =  sqrt  [ surface area of A / surface area of B ]  = 

sqrt [ 28 / 40.32 ]  =    sqrt [ 25/ 36]   =  5/6

Note that Volume of A  = (5/6)^3 * Volume of B

Note that we can set up the following  relationship :

Mass A              density * volume  of A

______  =         __________________            (cancel  the density)

Mass B             density *  volume of B 

Mass A              volume of A

______   =        ___________ 

Mass B             volume of B

Mass A           (5/6)^3 * volume of B

_______ =       _________________         (cancel volume of  B)

6912 g               volume of B

Mass A   =  (5/6)^3

______                                        (multiply both sides by 6912 g

6912 g

Mass A  =  (5/6)^3 * 6912 g    =   4000 g