Gold Cube Density Problem: Calculating Side Length for Double Mass

[LoveKnowledge]

1. A 19.3-g mass of gold in the form of a cube is 1 cm long on each side (somewhat smaller than a sugar cube). What would be the length of the sides of a cube having twice this mass of gold?



2. Density=mass/volume



3. I had help from a friend in which resulted with the following result/attempt but I am confused in regards to the foundations of how I solved the problem...I know while dimensions may be squared, weight and volume is cubed but I want to understand the solid foundations of the question...

1.26 cm. V1=1cm^3 which results in m1=19.3 grams, density=m/v=19.3 g/cm^3; m2=2x19.3=38.6 grams (density remains constant of 19.3 g/cm^3); V2=2V1=2 cm^3 resulting in each side from 2^1/3=1.26 cm for each side. It is important to remember than while the surface area proportions are squared, the volume and weight is always cubed."

 

[cyby]

The original information will actually give you the density of gold, which is 19.3g/cm^3. Knowing that the density stays the same, you just need to apply the density formula to find the volume, and then cube root that to find the length of each side.

If D = m/V, then V = m/D. Knowing that the second cube is twice as massive (38.6 grams), we can now apply the formula:

Volume = (38.6g/19.3(g/cm^3))

Not surprisingly, the volume is twice as big (2cm^3).

Since the formula for the volume of a cube is s^3, where s is the length of a side, we merely need to solve 2 = s^3.

 

[LoveKnowledge]

So the correct answer would be 1.5 cm rather than the 1.26 cm I provided for each side?

 

[cyby]

No. If each side is 1.5cm, then the Volume would be (1.5)^3 = 3.375cm^3, not 2cm^3.

The cube root of 2 is actually 1.2599..., which is about 1.26.

 

[LoveKnowledge]

K. I understand now. I need to square root it and that is where I was getting confused. I am going to save this so I can review and understand the principle more when I am done with my homework. :) Thanks you again for your help!