The obvious answer to what a graduated cylinder measures is of course the volume of liquids. A Class B graduated cylinder such as the one shown in the video is guaranteed to be accurate to 1%. This is good enough for most applications in the home or at work although not quite good enough for analytical chemistry methods.

Another use is to measure the amount of water displaced by objects. From this, one can deduce the volume of the object which can be particularly difficult if it is irregularly shaped. By knowing both the volume displaced by an object & its weight, you can calculate its density.

Aside from being an interesting exercise in itself, it was one of the earliest methods used to confirm whether metals for example are pure or adulterated. One such use is determining whether some is pure gold which was important for knowing whether official coinage was counterfeit or not.
 


 
The recommendations below 

If you think the object is 5ml (cc) or less, use a 10 ml graduated cylinder to confirm your assumption.
If you think the object is 12.5ml (cc) or less, use a 25 ml graduated cylinder to confirm your assumption.
If you think the object is 25ml (cc) or less, use a 50 ml graduated cylinder to confirm your assumption.
If you think the object is 50ml (cc) or less, use a 100 ml graduated cylinder to confirm your assumption.
If you think the object is 125ml (cc) or less, use a 250 ml graduated cylinder to confirm your assumption.
If you think the object is 250ml (cc) or less, use a 500 ml graduated cylinder to confirm your assumption.
If you think the object is 500ml (cc) or less, use a 1000 ml graduated cylinder to confirm your assumption.