Question

A steel bar has a mass of 4,000 kilograms and a volume of 0.5 cubic meters . Calculate its density. Write your answer as a whole number.

Answer 1

The equation for density is:

$D=\frac{m}{V}$

where the mass is in grams and the volume is in $cm^{3}$.

We are given 4,000 kilograms, and we know that there are 1,000 grams in 1 kilogram, so we need to multiply to convert to grams:

$4,000*1,000=4,000,000g$

We are also given 0.5 $m^{3}$, and we need to convert to $cm^{3}$. We know that there are 100 cm in 1 m, and since we are talking about cubic volume, we must also raise 100 to the 3rd power: $100^{3}=1,000,000cm$. So now we know that there are 1,000,000 $cm^{3}$ in 1 $m^{3}$. We need to then multiply 1,000,000 cm by 0.5 in order to find the volume that was given in the question:

$1,000,000*0.5=500,000cm^{3}$

So now that we have the correct units, let's plug them into the equation:

$D=\frac{4,000,000g}{500,000cm^{3}}$

$D=\frac{8g}{cm^{3}}$

So now we know that the density is 8g/cubic centimeter.