Question

A graduated cylinder contains 15 mL of water initially. A metal cylinder is placed in it and the water level rises to 25.5 mL. If the mass of the metal cylinder is 3.72 g, find the density of the metal cylinder?

Answer 1

The formula for the density, ρ, is (given a mass m and a volume V):

`\rho=(m)/(V)`

We know the volume in the graduated cylinder before and after the addition of the metal cylinder, so the difference is the volume of the metal cylinder:

`\begin{gathered} V=25.5mL-15mL \\ V=10.5mL \end{gathered}`

And the mass is given:

`m=3.72g`

So, the density is:

`\rho=(m)/(V)=(3.72g)/(10.5mL)=0.35428\ldots g/mL\approx0.354g/mL`

The density of the metal cylinder is approximately 0.354 g/mL.