Video: Knowing the Units for Physical Quantities

Which of the following is the correct unit for volume? [A] m [B] kg⋅m [C] kg/m³ [D] m² [E] m³.

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Video Transcript

Which of the following is the correct unit for volume? 1) meters, 2) kilograms times meters, 3) kilograms per meter cubed, 4) meters squared, and 5) meters cubed.

To answer this, first let’s have a look at what volume actually is. Volume is the amount of three-dimensional or 3D space occupied by an object. So let’s take any three-dimensional object, preferably a simple one to make life easier for ourselves, and see what the units of measurement are for its volume.

Let’s go with a cube. That’s quite easy to work with. So a cube has three dimensions as we know. The first one being its width. The second one being its length. And the third one being its height. Now because this is a cube and not a cuboid or any other 3D shape, the width, the length, and the height in this case are exactly the same as each other. However, that’s not the point. What we’re trying to do here is to work out how the volume of this cube is calculated. Well, we know that we need to multiply the width by the length by the height to get the volume of the cube. And since each one of these is a length, the standard unit of measurement is meters, in all three cases. Therefore, in order to find the volume when multiplying meters by meters by meters, or in other words, this is meters cubed. And so, our final answer is meters cubed.

Let’s quickly go through the other options to make sure that we haven’t done anything wrong. The first one, meters, well that’s just a unit of length. Whereas, we want a volume. So that can’t be right. So the second one, kilograms times meters, well we’ve got meters in there which is a length. But we’ve also got kilograms which is a measure of mass. Volume has nothing to do with mass. Volume is simply the amount of space. So that can’t be right either. The third one, kilograms per meters cubed, now we’ve got meters cubed in there which is a volume. But we’ve got kilograms per that unit volume. That’s actually a density. So that’s also not right. The fourth one, meters squared, that’s close. That’s basically like multiplying the width by the length of a 2D object. But that’s only the area. That’s not the volume. We need to multiply that area by a third dimension in order to get a volume. So that’s also not right. Which means that we can safely say that meters cubed is the right answer.

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