Volume Question?

Question

Im soo confused!

The density of mercury is 13.54 g/cm 3. Suppose you need 40 gm of mercury for an experiment. What volume of mercury do you need?

2.95 cm 3

541.60 cm 3

26.46 cm 3

Answer 1

m=dv

40 g=(13.54 g/cm^3)v

40g*1/13.54cm^3/g=v

2.95 cm^3=v

Answer 2

The first thing you need to know to answer this question is the definition of density. Density is defined as the mass of a material divided by volume of that material. Why is this a useful quantity? Well, the density of any material doesn't depend on how much of it you have. Increasing the volume of the material will also increase its mass, so the ratio will stay the same. Thus, density only needs to be calculated once for any given type of matter, and then can be used as a conversion factor between mass and volume, such as in this problem.

If you have any two of the three quantities in question (mass, volume, density) you can compute the missing third. You can very quickly tell how you need to put the given information together to get the answer by looking at units. Here we are given density, in units of mass / volume, and the mass. Since we need an answer in units of volume, we can divide mass by density:

mass / (mass / volume) = volume * (mass / mass)

= volume * 1 = volume

So, 40 gm / (13.54 g /cm^3) = 2.95 cm^3

Many physics problems are solved simply by looking at the units of given quantities, looking at the units of quantities that you want to solve for, and figuring out how arrange the given quantities to create the required units.

Answer 3

d=m/v

d=13.54g/cm^3

m=40g

v=m/d so

v=40g/13.54g/cm^3

v=2.95cm^3

Correct answer is a)

Answer 4

Density = mass / volume

13.54 = 40 / V

V = 40 / 13.54

V = 2.95 cm³