Question #651d1

1 Answer
Jul 22, 2015

Density: #"0.52 kg/m"""^3#


So, you know that you're dealing with an object that has a certain mass and a certain volume.

You weigh the object and determine that it has a mass of 22 kg. Likewise, you measure the volume of the object and determine that it occupies #"42 m"""^3#.

Density is defined as mass per unit of volume. In other words, density tells you what the mass of one unit of volume is for a given object.

SInce you measured the volume in cubic meters, the unit of volume will be #"1 m"""^3#.

So, to get the object's density, you need to determine what the mass of #"1 m"""^3# is. To do that, use the fact that you know what the mass of #"42 m"""^3# is

#1cancel("m"""^3) * "22 kg"/(42cancel("m"""^3)) = "0.5238 kg"#

If one cubic meter has a mass of 0.5238 kg, then the object's density will be

#rho = "0.5238 kg"/("1 m"""^3) = "0.5238 kg/m"""^3#

Rounded to two sig figs, the number of sig figs you used for your two measurements, the answer will be

#rho = color(green)("0.52 kg/m"""^3)#