Question

The density of aluminium is 2700kg/m^-3.calculate the mass of a block of aluminium which has a volume of 100cm3?

m^-3

Answer 1

The mass of the block is 0.270 kg.

Explanation:

There is one error in the problem as written up.
Density = mass/volume, therefore the units should be
either `(kg)/m^3 or kg*m^-3`.

This will require converting the volume units from `cm^3 " to " m^3.` I will use a method I call "multiplying by 1" that I have used since my first Physics class. You may go to this site for an explanation of my method:
https://socratic.org/questions/a-mile-is-5280-ft-long-1-ft-is-approximately-0-305-m-how-many-meters-are-there-i#469538

Converting `100 cm^3` step by step:
`100 cm^3 * ((1 m)/(100 cm))^3`
`100 cm^3 * (1 m)^3/(10^2 cm)^3`
`1*10^2 cm^3 * (1 m^3)/(10^6 cm^3)`
`1*cancel(10^2) cancel(cm^3) * (1 m^3)/(10^4*cancel(10^2) cancel(cm^3)) = 1*10^-4 m^3`

Density = mass/volume, therefore one algebraic operation will tell us that
mass = density*volume. So, the last step to finding your answer is

`"mass" = (2700kg)/cancel(m^3) * 1*10^-4 cancel(m^3) = 0.270 kg`

I hope this helps,
Steve