Iron has a density of 7.86 g/cm3. Calculate the volume (in dL) of a piece of iron having a mass of 4.07 kg .

Answer 1

First we have to find out how many ml are in dL. The unit dL means deciLiter, which is one tenth of liter. This can be expressed as:

1 Liter = 10 dL

For mL, or mililiter, there are 1000 ml in one liter. So, every Liter has 10 dL and 1000 mL. This ratio can be expressed as:

10 dL/ 1000mL = 1 dL/ 100ml

This makes sense because 10 dl equal one liter and 10 x 100 would be 1000 mL, which again is 1 liter.

The other unit 1cm³ is equal to 1 ml. (This is a common equivalent unit and one I would recommend remembering.)

So will use dimensional analysis to cancel out units:

4.07 kg (1000g / 1 kg) ( 1 cm³/ 7.86 g) (1 ml / 1 cm³)(1 dl/100ml) = 5.18 dL.