Understanding Volume of Cuboids and Cubes

In this video, we're going to look at how to calculate the volume of cuboids and cubes. For cuboids, the formula for volume is length times width times height, or in algebra, that would be v equals l times w times h. So if our cuboid had a length of 8cm, a width of 6cm, and a height of 5cm, then to find the volume, we're to just do the length of 8, multiplied by the width of 6 times the height of 5, which gives us 240 cubic centimeters. And don't forget that the units of volume are always cubed like this, because volume is in three dimensions. Now, moving on to cubes. Cubes are really just a special type of cuboid, so you could still use the cuboid formula of length times width times height. However, the special thing that makes a cube a cube is that the length, width and height are all exactly the same. So we can actually think of the formula as volume equals length times length times length, or length cubed. So if the length of the edges in our cube were 5cm, then dividing the volume would just do 5 times 5 times 5, or 5 cubed, which in either case would give us 125 cubic centimetres. Let's have a go at an exam style question now. So in this question we're told that a cuboid has a width of 5cm, a height of 7cm and a total volume of 350cm3. And our job is to find the cuboid's length. The first thing we're going to want to do here is write out the equation for the volume of a cuboid. So v equals l times w times h. Because we're trying to find the length though, we're going to have to rearrange the equation to get the length by itself, which we can do by dividing both sides by the width times height part, to get volume divided by width times height equals length. And then all we have to do is plug in the values from the question and solve it. So 350 divided by 5 times 7, which if you put it into a calculator will give you 10. so the cuboid has a length of 10cm. So that's the end of this video, if you found it useful then please do give us a like and subscribe, and if you want to do questions on this stuff or anything else in maths and science then head over to our platform by clicking on the link in the top right corner of this video.

And don't forget that the units of volume are always cubed like this, because volume is in three dimensions. Now, moving on to cubes. Cubes are really just a special type of cuboid, so you could still use the cuboid formula of length times width times height.

However, the special thing that makes a cube a cube is that the length, width and height are all exactly the same. So we can actually think of the formula as volume equals length times length times length, or length cubed. So if the length of the edges in our cube were 5cm, then dividing the volume would just do 5 times 5 times 5, or 5 cubed, which in either case would give us 125 cubic centimetres.

Let's have a go at an exam style question now. So in this question we're told that a cuboid has a width of 5cm, a height of 7cm and a total volume of 350cm3. And our job is to find the cuboid's length.

The first thing we're going to want to do here is write out the equation for the volume of a cuboid. So v equals l times w times h. Because we're trying to find the length though, we're going to have to rearrange the equation to get the length by itself, which we can do by dividing both sides by the width times height part, to get volume divided by width times height equals length. And then all we have to do is plug in the values from the question and solve it. So 350 divided by 5 times 7, which if you put it into a calculator will give you 10. so the cuboid has a length of 10cm.

So that's the end of this video, if you found it useful then please do give us a like and subscribe, and if you want to do questions on this stuff or anything else in maths and science then head over to our platform by clicking on the link in the top right corner of this video.

Transcript for:Understanding Volume of Cuboids and Cubes

Transcript for:
Understanding Volume of Cuboids and Cubes