Expert: Josh - 9/7/2006

Question
I have tried many attempts to solve this for Gen. Chemistry.  the question is:

a perfect cube of aluminum metal was found to weigh 620.0 g. The density of aluminum is 2.70 g/cm3. what are the dimensions of the cube?

I worked the problem to find the volume first and got 230.0 cm.  I just don't know where to go from there.  The instructor gave us the formula of cube root of volume.  help!

Answer
Hi Lori,

Don't panic. Let's work this out step by step.

Density = Weight/Volume.

Given Density=2.70 g/cm^3 and Weight=620.0 g, Volume=Weight/Density=620/2.7 is approximately 229.629 cm^3....[#1]

(Important note: cubic centimeter represents a three-dimensional volume)

Suppose the side of a cube has dimension "x". The volume of a cube is simply x*x*x=x^3. ....[#2]

Equating the volume in [#1] with expression [#2], we get x^3=229.629. We seek a value x, such that when multiplied by itself three times, it yields the volume 229.629 [cm^3].

The answer is given by the cube root of 229.629629....

You can use one of two buttons on your calculator.
[x^y]
[x^(1/y)]

For the former, you enter "229.629", then press the button and enter "1/3" and press [answer]

For the latter, you enter "229.629", then press the button [x^(1/y)]....check the menu, you may need to press the shift key or something, each calculator is different.... and then enter "3" and press [answer].

The answer is approximately 6.123 cm.