Hi, I am Eric Stone from South Burlington High School in South Burlington, Vermont, here for About.com. Today, we are going to talk about the volume and area of a right cylinder.The basic idea behind a right cylinder is that you have a circle, and that circle travels through space and creates a height. Now, a cylinder has some very important attributes that we need to define before we can find the area or the volume. First, the radius. The radius of a cylinder is the distance from the center of the circle at one end out to the edge. The height is going to be defined as how far that circle travels through space.The formula for the volume is, quite simply, take the area of the base -- whatever it is, in this case a circle -- and multiply it times the height. Now, I need to know how to find the area of the base, or in this case, the area of a circle. Well, the area of a circle is defined as pi-r-squared. So, to find the volume of a cylinder, all I need to do is take pi-r-squared and multiply it times the height.Surface area is a little more complicated. Basically what you want to do is you want to find the area of this -- the circle on the top -- the area of this, which is the circle on the bottom, and then, you also want to find the most difficult part, which is the area of the part that makes up the walls of the cylinder.

Sometimes using a piece of paper helps. Here is a piece of paper that I have shaped like a cylinder. Now, if I want to know the area of this, the best way to think about it is to unravel it -- to that. What do you see? You see a rectangle. The rectangle is defined, then, usually by length and width. For our cylinder, the width of the rectangle is just going to be the height of our cylinder -- there it is. The length is going to be the distance around my cylinder like so. And in geometry or algebra or any math class, that distance around a cylinders base is very important, we call it the circumference.

So our length turns into the circumference of a circle. The formula for the circumference of a circle is equal to two-pi-r. All I need to do then, is take 2-pi-r and multiply it times h.

So, if I want to find the total area of a cylinder, all I need to do is add up the area of the circle on top, the area of the circle on the bottom, and the area of the part that makes up the walls. So it will be pi-r-squared for the circle at the top, plus pi-r-squared for the circle at the bottom, plus 2-pi-r-h for the part that makes up the walls.

Pi-r-squared plus pi-r-squared is 2-pi-r-squared, and here comes the formula that you all know and love. The area of a cylinder is equal to 2-pi-r-squared plus 2-pi-r-h.

Thanks for watching! To learn more, visit us on the web at About.com.

Sometimes using a piece of paper helps. Here is a piece of paper that I have shaped like a cylinder. Now, if I want to know the area of this, the best way to think about it is to unravel it -- to that. What do you see? You see a rectangle. The rectangle is defined, then, usually by length and width. For our cylinder, the width of the rectangle is just going to be the height of our cylinder -- there it is. The length is going to be the distance around my cylinder like so. And in geometry or algebra or any math class, that distance around a cylinders base is very important, we call it the circumference.

So our length turns into the circumference of a circle. The formula for the circumference of a circle is equal to two-pi-r. All I need to do then, is take 2-pi-r and multiply it times h.

So, if I want to find the total area of a cylinder, all I need to do is add up the area of the circle on top, the area of the circle on the bottom, and the area of the part that makes up the walls. So it will be pi-r-squared for the circle at the top, plus pi-r-squared for the circle at the bottom, plus 2-pi-r-h for the part that makes up the walls.

Pi-r-squared plus pi-r-squared is 2-pi-r-squared, and here comes the formula that you all know and love. The area of a cylinder is equal to 2-pi-r-squared plus 2-pi-r-h.

Thanks for watching! To learn more, visit us on the web at About.com.

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