A cylinder is a three-dimensional object that has two circular or elliptical flat ends and one curved side. One way to visualize what this means is to think of a two-dimensional circle drawn on a piece of paper and cut out. If the exact same two-dimensional circular shape were to be drawn on a vast number of different pieces of paper, then stacked perfectly on top of each other, they would form a cylinder.

**Finding the Surface Area of a Cylinder**

Hopefully the above thought experiment will be helpful in learning how to think about surface area. The equation used is fairly simple:

Surface Area = 2 x π x r x (r+h)

This equation can be divided up into two different parts to make it easier to conceptualize. The surface area of one end, which can be calculated as the area of a circle, or A = π x r^{2}, and the surface area of the side, which would be calculated using the equation: A = 2 x π x r x h.

Sound confusing? It’s really not. Let’s take a look at an example to see just how easy it really is.

Assume that the cylinder in question has a radius of 2, and a height of 7. We already know that the equation S A = 2 x π x r x (r+h) yields the surface area, so it’s as simple as plugging in the given dimensions and following the order of operations to get the correct answer.

If S A = 2 x π x 2 x (2+7), the first step is to add 2 + 7 to get S A = 2 x π x 9, which can be simplified to 36π. If a numerical estimate is required, simply multiply 36 by 3.14 to get 113.04.

**Finding the Volume of a Cylinder**

The volume of a cylinder is almost as easy to find as its surface area, and requires only the same two measurements. Here’s the equation: Volume (V) = π x r^{2} x h.

Understanding why requires that we again consider the nature of a cylinder as a three-dimensional shape. Recall that the area of a circle can be found using the equation A = π x r^{2}, and that a cylinder is more or less a series of two-dimensional circles placed on top of each other. Since “h” is equal to height in this equation as well, it makes good sense that it would be multiplied by the area of the circle that forms one end to find the overall volume.

Let’s go back to our example. To find the volume of a sphere with a radius of 2 and a height of 7, we simply need to plug the numbers into the equation: V = π x 2^{2} x 7. It’s easy enough to figure out that 2 raised to the second power is 4. Multiply that by 7, and we get the answer: 28π. Again, if a numerical estimate is needed for further calculations, simply substitute 3.14 for π to get 87.92.

These equations can be applied in all sorts of real-world scenarios, from determining how much water would be required to fill a cylindrical vase, to trying to guess the number of marbles or candies in a cylindrical jar at a county fair.