Can you please help me understand this type of conversion?

Hi,

I am having a very hard time understanding the process of converting units in this case. I have indeed looked at a few worked solutions but I still don't quite understand. Here is my conversion question.

How do you convert cm^3 to cm^2. I know - you can't because one is a unit of volume and one is a unit of area.
But... Say I have exactly 32 cm^3 of apple juice (32 mL) and I spill it out on to a 12 in^2 table (the liquid stops at all four sides and doesn't spill off). I now know the liquid covers a 12 in^2 surface. How deep is that layer of apple juice? Or... how do I go from that 32 mL container to that 12 in^2 surface? I just don't get it.
I DO know that I must make use of the density of apple juice (or water at 1g/mL) and I DO know that I can use these formulas, right?

V=ST (Volume = Surface Area times Thickness)
and D = M/V

Thank you in advance for any help or light...

Re: Can you please help me understand this type of conversio

1) Look up "meniscus" (not the knee - the other kind) This should persuade you that your task is even more difficult than you may have imagined.

2) Since we're already a little off, I am having trouble imagining that the density of water vs. apple juice will be significant.

3) Having said that:

\(\displaystyle 32\;cm^{3}\cdot \left(\frac{1\;in}{2.54\;cm}\right)^{3}\;=\;1.952759811\;in^{3}\)

\(\displaystyle 1.952759811\;in^{3}\;=\;(12\;in)^{2}\cdot Depth\)

\(\displaystyle Depth\;=\;0.013560832\;in\)

I'll let you worry about the significant figures.

I suspect you found this difficult ONLY because you panicked.