A cube has a mass of 30 kilograms. If the volume of the cube is 0.02 meters cubed, what is its density?
Okay, so let’s say that this is the cube we are asked about in this question. We are told the mass and volume of this cube. Let’s call the mass of the cube capital 𝑀. And we are told that the cube has a mass of 30 kilograms, so 𝑀 is equal to 30 kilograms. We are also told that the volume of the cube is 0.02 meters cubed. So if we call the volume of the cube 𝑉, then 𝑉 is equal to 0.02 meters cubed.
Given this information, we are asked to find the density of the cube. We can do this by first recalling the general formula for the density of an object. We usually call the density of an object lowercase 𝜌, which is a Greek letter that looks a bit like a 𝑝. The formula for an object’s density is then 𝜌 is equal to 𝑀 divided by 𝑉, where 𝑀 is the mass of the object and 𝑉 is the volume of the object.
So in order to find the density of our cube, we need to divide the mass of the cube by the volume of the cube. Since we are told these values in the question, we can simply substitute in these numbers to the formula we have just recalled. Here, the mass of our cube is 30 kilograms and the volume of our cube is 0.02 meters cubed. This means that the density 𝜌 of the cube is equal to the mass, which is 30 kilograms, divided by the volume, which is 0.02 meters cubed.
We can simplify this fraction by first separating the numerical part from the unit. So the density 𝜌 is equal to 30 divided by 0.02, and the units are kilograms over meters cubed or kilograms per meter cubed. These are the correct units for density, so we can leave these as they are. We can then simplify the numerical part by working out that 30 divided by 0.02 is equal to 1500. So we have now found the density of the cube. And we can give 𝜌 equals 1500 kilograms per meters cubed as our final answer to this question.