Dimensional Analysis: A high school senior weighs 135 lbs prior to swimming season and has a density of 1.10 g/cm3. Halfway through the season, her friends compliment her on her excellent shape. Her density has increased to 1.20 g/cm3 and she has gained 5 lbs. Use 2 separate calculation set-ups to illustrate why she receives the compliments despite gaining the weight!

Question

anonymous · Answer

Ok, looks like you're to make a before and after comparison of her volume. It doesn't specify which units to express the answer in, so that's your choice. I'd personally convert all the weights to grams and compare the two volumes in terms of cc's.

anonymous · Answer

what do you mean? how would that prove that she hasn't grown fatter?

anonymous · Answer

Fatter means more volume. Also fat has a lower density than muscle, so if she gained weight and density then that means the majority of the weight gain was from increased muscle.

anonymous · Answer

Just knowing that her density increased tells you that she lost fat or at least gained more muscle than fat, but in order to tell how her friends noticed her slimmer figure, you'll have to calculate the before and after volumes.

anonymous · Answer

okayy. Thanks. I think i got it :)

anonymous · Answer

Ok, let me know what you get for the two volumes so I can check my work.  ;-)

anonymous · Answer

I got 55718g for her first volume and 52966 after swimming

anonymous · Answer

That's slightly different from what I got, but that's likely due to round-off error somewhere. Also (assuming the 5 pounds of weight gain can be assumed to be accurate to 5.00) then those numbers should be rounded to 3 sig.figs.
Lastly, those are volumes and the units are cm^3 not g.

anonymous · Answer

What conversion factor did you use for pounds to grams?

anonymous · Answer

454 g to 1 lb

anonymous · Answer

Ok, that's probably fine for this level of accuracy. I used 453.59 - Ideally, you'll want to multiply by a number with more sig.figs than you plan to round to. e.g. If you know your answer is going to have 3 sig.figs. then use an accuracy of at least 4 sig.figs. in all your intermediate calculations to minimize round off error.

anonymous · Answer

Might also want to convert cc's to liters so the numbers aren't as cumbersome.
The two volumes would then be 55.7 liters and 52.9 liters which is a little easier on the eyes.