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jdavid3 · Feb 28, 2011, 10:01 AM

A chemist pours 200 grams of a liquid (density = 2.5 gm/mL) into a cube beaker with 5 cm edges and a graduated cylinder with a base radius of 5 cm and a height of 5 cm. What is the fraction of the liquid that needs to be poured into the graduated cylinder so that the height of the liquid is the same in both containers? Is the height of the liquid in the cube beaker less than or greater than 1 cm? I need help FAST! Please help me and show all steps.

Unknown008 · Feb 28, 2011, 10:29 AM

This is no chemistry problem but math problem. Please note also that we do not do your homework.

The volume of solution can be obtained using the density.

2.5 g -> 1 mL
1 g -> 1/2.5 mL
200 g -> ? ML

Then, the volume of solution in the beaker is given by:

$V = Ah$

Where A is the area of the base (square) and h is the height of the solution.

The volume of solution in the graduated cylinder is given by:

$V = Ah$

Where A is the area of the base (circle) and h is the height of the solution.

Both h should be equal, and the total volume has to be the initial volume of solution you used. You can find the area of the bases of the beaker and the cylinder from the information given.

Can you find the volume fraction?

jdavid3 · Feb 28, 2011, 11:24 AM

This is not a homework problem but a problem for a contest. You are allowed to solve it for me. Please do so with numbers.

jdavid3 · Feb 28, 2011, 11:26 AM

This is not a homework problem but a problem for a contest. You are allowed to solve it for me. Please do so with numbers. Thank you for your help.

jcaron2 · Feb 28, 2011, 08:25 PM

Homework, contest, whatever. Presumably the point is for you to show that YOU know how to do the problem, not that you know how to get someone else to do it for you. Unknown008 gave you pretty much everything you need to know to solve the problem, you just need to apply yourself a little.

If there's a specific part you're still stuck on, feel free to ask, but don't just blindly continue to ask us to solve the entire thing for you. Show us that you're putting some effort into solving it yourself.

So to start with, what's the total volume of liquid (the question mark near the top of Unknown008's answer)?

Also, remember that 1 ml is the same thing as 1 cm^3.

jdavid3 · Mar 1, 2011, 05:24 AM

The volume of the liquid is 80 ml. The volume of the cube beaker is 125. The volume of the cylinder is 125pi (392.7). I got that far but I am stuck after that.

Unknown008 · Mar 1, 2011, 06:28 AM

Okay, finding the volume of the beaker and that of the cylinder only shows you that they won't be full, even if all the solution is poured into one.

Use what I told you, let the height of the fluid be h in each container. Can you find the volume of fluid in terms of h?

jcaron2 · Mar 1, 2011, 07:16 AM

Excellent! Now you just need to do as Unknown008 said. If you call the volume of liquid in one container V1, and the volume of the other V2, you know that V1 + V2 = 80 cm^3. Just plug in the appropriate formulas for V1 and V2 in terms of unknown h (you already did it for a known h of 5 cm for each), then solve for h.