Did you know?

The density triangle isn't the only memory tool used by physicists. There is another triangle, known as the V-I-R triangle, which can be used in a similar manner. It can be obtained simply by replacing D, M, and V in the density triangle, by I, V, and R, respectively. Using the same multiplication and division rules, the V-I-R triangle can help memorize the three formulae that comprise Ohm's law.

Every physical object is made up of matter. As such, it has three measurable quantities associated with it, namely - density, mass, and volume. The following are the definitions for each. 1) Mass: The total amount of matter present within an object or a body is known as its mass. Its S.I. unit of measurement is kg. Note that mass is different from weight, which represents the gravitational force of attraction on an object. For example, a person will weigh less on the moon due to its weaker gravity as compared to Earth, but would have the same mass in both the places. 2) Volume: The overall space occupied by a body in a 3D space is known as its volume. Volume, thus, represents the body's expanse in all three dimensions, represented by its length, width, and height. The S.I. unit for each of these is meter (m), and since volume is a product of the three, its unit is m³ 3) Density: The density of an object is the measurement of its compactness. Basically, it tells you how closely crammed matter is within that object. Mathematically, it is defined as the mass per unit volume of a body. From these definitions, it is clear that density is a function of both the mass as well as the volume of an object. Its mathematical equation comprises both these quantities. By rearranging the terms of this equation, two more equations can be derived - one to calculate the mass and another to calculate the volume. So effectively, if you can remember any one of them, you can easily find out the remaining two. However, the downside to this is that, if you get the first one wrong, then the remaining two shall also go wrong. To avoid such a situation, the density triangle was conceived.

An old Chinese proverb - I hear and I forget, I see and I remember, I do and I understand. The density triangle is in keeping with the first part of this proverb. It gives you a visual representation, which helps you easily remember the three density triangle formulae or equations. The following is what a density triangle looks like. The M on top represents the mass of a body, while the D and V at the bottom represent its density and volume, respectively. Using it, three density triangle equations can be derived, one each for calculating the mass, density, and volume of an object. Hence, it is also sometimes called the mass volume density triangle. To obtain these three equations, all you need to do is memorize this one triangle, and then use the procedure described below. 1) Formula for Density To get the formula for density, simply cover the 'D' part with your fingers. Now what remains is M and V. Notice that M is above and V is below, separated by a horizontal dividing line. Thus, M is to be divided by V, giving us the following formula for density. D = M ÷ V 2) Formula for Mass Likewise, to calculate the mass of an object, cover the 'M', as shown in the image. The remaining part of it shows D and V adjacent to each other. This indicates that D has to be multiplied by V, giving us the following equation for the mass of an object. M = D × V 3) Formula for Volume To work out the formula for the volume of an object, cover the 'V' in the density triangle. What remains is M and D, with M above and D below, separated by a horizontal dividing line. Thus, we get the following formula for the volume of an object. V = M ÷ D

Look at the Chinese proverb in the previous section again. The last part says, 'I do and I understand'. This is very important, because unless you bring the use of the density triangle into practice, you won't be able to fully understand how to use it. To help you in this endeavor, in the following lines, we present to you four fully-solved examples. It is advised that you try to solve them on your own before going through the solutions, to get a better grip on this topic.