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First, try to get the units the same for all the factors in the problem.
So, since the density is g/cm^3, convert the mass of the gold to grams. 0.715kg is converted to grams by multiplying by 1000. So 0.715kg becomes 715 grams.
Now you can express the problem as a ratio and solve it....
19.3g/1cm^3 ~ 715g/Xcm^3. (a/b~c/d & solve for d)
Now solve: Multiply both sides by Xcm^3 which gives:
19.3g*Xcm^3/1cm^3 ~ 715g*Xcm^3/Xcm^3....
simplify to get:
19.3g*X =715g
divide each side by 19.3 to get
37.0466cm^3 which is the volume of gold with a mass of .715kg.
Take the cube root of this volume to get the length of a side of a cube of gold with this mass.
This gives you an edge length of approximately 3.402 cm.
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