What is used to classify volcanoes based on the strength of their eruptions?

The answer you are looking for is the VEI scale, also known as the Volcanic Explosivity Index. The scale ranges from 1-8. Volcanic eruptions are classified due to how much volcanic material is ejected into the atmosphere, the height of the plume cloud, and how long the eruptions last. For example, the eruption of Mount Tambora in 1815 was a VEI 7 and caused the year without a summer. Volcanic eruptions in VEI 6 and 7 ranges are really rare, but VEI 8 eruptions are the rarest. VEI 8 eruptions are known as super eruptions, and they happen around every 100,000 years. Sorry, I got a little bit carried away. But, anyways, the VEI scale is the correct answer.  

other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. the si derived unitsfor these derived quantities are obtained from these equations and the seven si base units.