Question

The density of a substance determines whether it will float or sink in a liquid. The density of water is 1 gram per millimeter. Any object with a greater density will sink and any object with a lesser density will float. Density is give by the formula d=m/v, where m is mass and v is volume. Here is a table of common chemical solutions and their densities.

Answer 1

Plastics vary in density when they are manufactured; therefor, their volumes are variable for a given mass. A tablet of polystyrene (a manufactured plastic) sinks in water and alcohol solution. The tablet has a mass of 0.4 grams. What is the most its volume can be?

Answer 2

What's the density of that polystyrene tablet?

Answer 3

1.40, right?

Answer 4

I'm not quizzing you, we need to know the density so we can calculate its volume.

Answer 5

oh. then it's 1.40... i think

Answer 6

is calcium chloride polystyrene?

Answer 7

i'm not sure...

Answer 8

Isaiah, what do you mean?

Answer 9

density=m/v
d<0.92(from the alcohol)

m/v<0.92

m/0.92<v(volume is not negative, so we don't have to worry about switching the signs)

0.4/0.92<v

0.43<v

Answer 10

I would have had the solution earlier, but the equation editor crashed on me;/

Hi again, by the way!

Answer 11

lol hi. still reading your awesome explanation lol

Answer 12

What is the least it's volume can be, @danielcb114 ?

Answer 13

The volume cannot be 0, so we can say that the volume is 0<V<0.43

Or you can use interval notation, if you've seen it; if not, you'll probably see it soon enough.

Answer 14

Also, for the first problem, you only stated the 70% isopropyl alcohol. What about the concentrated calcium chloride (which floated). Also, what is the least it's volume can be (relating to the first question)?

Answer 15

whoa...what? 0<v<0.43? isn't that...still 0?
so basically what you are saying is that 0<v<0.43 is a... erhm...nicer way...of saying 0? is that it?

Answer 16

Basically, yes. In calculus we would say that the volume is dv; a differential value that's infinitely small, but not 0; but that's not what they're looking for, obviously.

It depends on what kind of notation they want. There's interval notation, inequality notation, verbal, set notation...what did your teacher/the book show you?

Answer 17

lol not in calculus yet. the book..?
it's a worksheet, so i'm VERY confused on this one. lol.

Answer 18

The safest thing to put is that the volume of the plastic has to be between 0 and 0.43; the smallest value it can be is anything that's not 0, essentially. You can't say any number; if you say the smallest is 0.1, I can say 0.01 is a legitimate volume, then 0.001, etc.

Answer 19

btw, how did you get zero?

Answer 20

Well, look back at the equation. We know that the volume is less than 0.43. Based on the equation alone, the volume could be -5000; but we know that, in real life(and in the world problem) you can't have negative volumes. You also can't have things with 0 volume; so we can exclude all negative values and 0.

Answer 21

okay.oh i see.

Answer 22

Also, I didn't see calcium mentioned in the original problem. That problem is very similar to the other problem though; you should be able to solve it in the exact same way, except you might have to flip the sign around.

Answer 23

okay.

Answer 24

wait... but shouldn't it be
@danielcb114