Density help....?

Question

Need help with one of the question... on denstiy.. thank you


An ice cube with a volume of 50.0ml and a density of 0.8 g/cm3 floats in a liquid with a density of 1.30 g/ml. What volume of the cube is submerged in the liquid?

Answer 1

Whoa, this is quite a question. I'm going to go out on a limb on this one, so someone please back me up or prove me wrong:

First of all, 1 mL = 1 cm3, so the density of the ice cube is 0.8 g/mL. Now everything is in the same measurement. Since we have a 50.0mL cube with density 0.8 g/mL, the cube has a mass of:
50.0mL * 0.8 g/mL = 40.0 g
Now, since the volume of the cube is 50.0mL, the length of one side is:
cbrt (50.0) = approximately 3.7cm
Thus, the area of the bottom surface of the cube is approximately:
13.7cm2
... I'm getting lost. Is there a ratio you learned that you are not telling us? I know that in water, having a density of 1 g/mL, approximately 9/10 of the ice remains submerged (the reason icebergs are so dangerous to ships).

Answer 2

The liquid displaced by the ice cube must equal the weight of the ice cube.

0.8 g/cm^3(50 mL) = 40 grams [1 cm^3=1mL]

40 g / 1.3 mL = 30.8 mL of the ice cube will be submerged.

Answer 3

Let ice cube =I i and liquid =L, then Vidi=vLdL and VL+ViDi/dl, you must either convert density of the ice cube to g/ml or that of liquid to g/cm3

Answer 4

you can think of this as "how much of the liquid weighs what the whole ice cube weighs".
The ice cube weighs 50 cc * .8 g/cc = 40 grams (1 cc = 1 ml)

So, how much of the liquid weighs 40 grams?
the answer is, 40 g/ (1.3 g/cc) = 30.76 cc (or 30.76 ml)