in this video we will be looking at the volume of a cone but first can you remember what the air what the formula is for volume well volume is equal to the area of the base times the height and so if we were looking at a cylinder which we have here on the right then we could use the base for example as the circle at the bottom and then what we would do is we would drag that circle up to the very top and that length would be the height and so the final for for that cylinder we would say volume is equal to so the area of the base would be a circle so that would be pi r squared and then the height we would use would be this height over here so you'd do something like that but that's a cylinder in this video we're talking about a cone but they do have a similarity would you say that you could put more water in the cylinder or could you put more water in the cone if their radius and their height is the same oh it's obvious that you would be able to fit more water in the cylinder because all of this part over here has been taken away when you're looking at a cone and so mathematicians have come up with a rule that we can use whenever we have a pyramid kind of shape now a pyramid kind of shape is anything where it starts off wide at the bottom and then ends up narrow or at a specific point at the top so what mathematicians and you might remember this from when we did the cube and the pyramid we said that all you have to do at the end is divide your answer by three so what you could do is you could imagine this cylinder over here you would get that one's answer and let's say the volume was 30 then for the cylinder you would just say 30 divided by three and so the volume of a cone is equal to the following so there it is at the bottom it says the area of base times height so you do that and that would be the same as for a cylinder and then that little line is me trying to say divide so you then say divided by three and so in your in class your teacher might use the following she might say or he or she might say volume is equal to a third a times h now what this all means and this is the same as what we saw with a cube and a pyramid what this says is that the the a well that's the area of the base the h that's the height and the third well that's the same as dividing by three so in summary a cone and a cylinder almost have the same volume it's just that the cylinders volume will be one third sorry the cones volume will be one third of the cylinder so you pretend it's a cylinder and then you'll just divide your answer by three and so let's put that into practice and let's actually work out the volume of this one over here so we know that the volume of us of a cone is area of base so the base is this part over here and so the area of a circle is just pi r squared and then we're going to times that by the height now what height do we use well for volume you're always going to use this height over here that central height that's going right from the top of the pyramid down to the middle it's only when we're doing area that we have to try use this one over here because area is all about the outside volume is more interested on the inside and so if we had to go fill this in so that's just going to be height so we're going to go pi the radius well that's 5 the height is 10. now if we did that that would actually be a cylinder but then because it's a cone we have to just remember to divide our answer by 3. and if you had to go do all of that on the calculator you end up with a final value of 261.8 now i haven't given units but let's say it was centimeters then we would use centimeters to the power of 3 because volume is always to the power of 3.