A refractories technologist often has to work out the mass of material required to make a product.  This is done by measuring the mould and calculating the volume.  If you get the volume in cubic metres you can multiply by the density of the material and get the mass required in tons.  If you measure the volume in litres you get the mass required in kilograms.  To get the mass required in litres you have to measure in decimeters.  The metric system would have been more logical if the measure of weight called a gram was actually a kilogram and the measure of length called a metre was actually a decimeter then it would be more logical.  (Using the Imperial system is extremely difficult and ridiculously illogical.)

The volume of a cube is the length of one side cubed.  The volume of rectangular shapes is the length times the width times the height.  Probably the commonest calculation of volume you will do is that of a pipe.  I find that the easiest method is to measure the outer diameter in millimetres, divide by 200 to get the radius in decimeters.  Then apply pi r squared to get the surface area in square decimeters.  Do the same thing inside diameter.  Subtract the inside diameter from the outside diameter.  Then multiply by the length in decimeters.  The result is the volume in litres would you multiply by the density of the material to get the weight in kilograms.

If the density of a material is given as 1.2 you can interpret it as 1.2 kg per litre or 1.2 tonnes per cubic metre or 1.2 g per millilitre.  

When i buy a scale which at the press of a button can be converted from measurement in grams, to ounces, pennyweight or other archaic weight measurements, I immediately disable that button.  A lot of hard work can be destroyed by inadvertently pressing that horrible button.

The density of materials can be determined by weighing and measuring and dividing the mass by the volume.  For irregular shaped materials the volume can be determined by measuring the volume by displacement of water.  Weigh the sample.  Place a bucket of water on top of the scale and tare it.  Suspend the sample with a thin nylon apparatus.  Immerse it in the bucket of water making sure it is fully submerged and not touching the bottom of the bucket.  The weight in grams shown on the scale is the exact volume in millilitres.