Calculating dimensions of a cylinder

0:00- [Narrator] The volume of the cylinder is 80 pi cubic centimeters. Find the height of the cylinder. Pause this video and have a go at that. All right. So let's just remind ourselves how we would calculate the volume of a cylinder. The volume is going to be the height times the area of the base.

0:18And then what's the area of the base? Well, that's going to be pi times the radius of the base squared. Now what do we know? We know that the volume is 80 pi cubic centimeters. So we could write 80 pi is equal to the height. That's what we need to solve for, times pi.

0:36And then the radius right over here, they're telling us that it is four. Now we can make sure that all of our units are matching up. If we wanted to, we could write our units here, but it's nice that this is in centimeters, this is in cubic centimeters. We'd have to do some conversion if one of these were in, say, meters or something else.

0:51But we can see it's all in centimeters or centimeters cubed. So we can just say the radius is four and of course we're going to want to square it. And this is nice because when you look at this, there's only one unknown here. There is h. We know what pi. Pi is a number and everything else is a number as well.

1:09Now to solve for h, we could immediately divide both sides by pi, in which case, you'd lose the pi on both sides there. So you would get 80 is equal to four squared, which is equal to 16h. And then we could divide both sides by 16. Divide both sides by 16. 80 divided by 16 is five.

1:28So we get five is equal to h and it's going to be five centimeters. So five. So let me just write this. This is right over here, is five centimeters and we are done.