How to Find the Volume of a Cylinder Math with Mr J

Welcome to Math with Mr. In this video, I'm going to cover how to find the volume of cylinder. And remember, volume is the amount of space three-dimensional object takes up. So, let's get into our example here where we have cylinder with given height of 8 in and our base has given radius of 3 in. So, that's the information we need in order to calculate volume of cylinder. Now, we have two formulas at the top of our screen here. They look different, but they mean the exact same thing. So, the top one says volume equals capital * So, that capital means the area of the base * which is height. Now, the formula below that says volume equals pi squared. So, pi * radius squared * height. Now, pi squared, that's the formula for the area of circle. So, in the case of this cylinder, our base is circle. So, the area of the base, that capital expanded out to the formula we're going to use pi squared, would give us that formula that's below. So, they mean the same thing, they just look little different. So, now we plug in our givens, that height and radius of the base, into our formula in order to calculate the volume of this cylinder. So, we will come to the side, we'll rewrite our formula, pi * radius squared * height. Then we will plug in. So, pi * the radius of our base, which is 3 in, is squared * the height of 8 in. So, So, time to simplify and work our way down to the final answer. So, we will do one step at time here. So, 3 squared would be first, which means 3 * 3, and that gives us 9 * the height of 8. So, next step, we could do 9 * 8, which is 72. And we multiply that by pi. So, put the 72 before the pi because typically when you multiply something by pi, you put the number first. And multiplication is commutative, so you can switch the order of things and still get the same answer. For example, 3 * 2 is 6 and 2 * 3 is 6. It doesn't matter the order. So, 72 * pi, as far as that goes, I'm going to use the pi button on my calculator when punch this in. If you are using the approximate or rounded pi, 3.14, which is common to do, you may get slightly different answer than me, but you are still correct. You just used the rounded version of pi. So, once punch that in, get pretty long decimal there. So, I'm going to round it to the hundredths place. Again, I'm rounding my answer to the hundredths place, and get 226 and 19/100. And this is volume, so we use cubic inches. Or, I'm sorry, cubic whatever the unit of measure is. And in this case, we were working with inches. So, cubic inches. So, volume equals 226 and 19/100 cubic inches. So, there's how you find the volume of cylinder. We found the area of the base and multiplied it by the height. Now, our base was circle. So, we used pi squared in order to calculate the area of our base and multiplied it by the height. hope that helped. Thanks so much for watching. Until next time, peace.