Question

A graduated cylinder has a mass of $ 50 \cdot g $ when empty. When $ 30 \cdot mL $ of water is added, it has a mass of $ 120 \cdot g $ . If a rock is added to the graduated cylinder, the level rises to $ 75 \cdot ml $ and the total mass is now $ 250 \cdot g $ . What is the density of the rock?

Answer 1

Hint: Density is the ratio of mass and volume of the substance. It is the measure of how densely the particles of a substance are packed. For the given problem, mass and volume of the rock is needed to be found and then mass has to be divided by the volume to obtain density.

Complete answer:
The given mass of the system before the addition of rock is $ 120 \cdot g $ and the mass after the addition of $ 250 \cdot g $ . So, the final mass of rock can be calculated as the difference between both the values.
 $ \eqalign{
  & mas{s_{rock}} = mas{s_{after}} - mas{s_{before}} \cr
  & mas{s_{rock}} = 250 \cdot g - 120 \cdot g \cr
  & mas{s_{rock}} = 130 \cdot g \cr} $
Similarly, the initial volume of the system before the addition of rock is given as $ 30 \cdot mL $ and the final volume of the system after the addition of rock is given as $ 75 \cdot ml $ . So, the volume of rock can be calculated as the difference between both the values.
 $ \eqalign{
  & volum{e_{rock}} = volum{e_{after}} - volum{e_{before}} \cr
  & volum{e_{rock}} = 75 \cdot ml - 30 \cdot ml \cr
  & volum{e_{rock}} = 45 \cdot ml \cr} $
Now, the density of rock can be calculated as the ratio of mass and volume,
 $ \eqalign{
  & density = \dfrac{{mass}}{{volume}} \cr
  & density = \dfrac{{130 \cdot g}}{{45 \cdot ml}} \cr
  & density = 2.9 \cdot g/ml \cr
  & density = 2.9 \cdot g/c{m^3} \cr} $
Hence, the density of rock is calculated as $ 2.9 \cdot g/c{m^3} $ .

Note:
The density is expressed in the unit of gram per millilitre or gram per centimeter cube. Centimeter cube is equivalent to a millilitre. The first given mass of the cylinder has no direct role in this calculation, so don’t get confused.