The Cylinder - Not a Round Rectangle...But, Kinda...

We depend so much on the shape of the cylinder.  If you truly understand what a cylinder is, you will see that we use it everywhere.  To help understand what a cylinder is, I think it is best to imagine one.  I think of a can of food.  A can is a cylinder.  If you look at it from the side, it looks like a rectangle, if you look at it from the top, it's a square.  That is the basics of a cylinder.

Now that I've pointed out one example of a cylinder, look around and see what other examples you can think of.  How about an unsharpened pencil?  A pizza is a very flat cylinder.  Any pole or even the columns on old buildings can be cylinders.  It's pretty obvious that this shape is important to us.  This is why it's important to understand the basic math behind the cylinder.

First, we'll look at the volume of a cylinder.  Since volume measures the 3-D aspect of the shape, we need to know the area of the base, then multiply that by the height.  The base is a circle, so to find the area we multiply Pi x R².  Pi is a constant that is approximately 3.1416.  R is the radius of the circle.  Once we find the area of the base circle, we multiply that by the height to find the volume.  The total equation is Pi x R² x H.

Online Calculator for Cylinder Volume
Online Calculator for Circle Area
Surface area of a cylinder is also important to know.  The surface area is the amount of area on the surface of the cylinder.  This would include the area of the circle on the base, and the area of the circle on the top of the cylinder, as well as the rectangle that wraps around the body of the cylinder.  So the total surface area of the two circles would be 2 x Pi x R². The area of the rectangle that surrounds the body would be found by multiplying the height of the cylinder by the circumference of the base of one of the circles.  The circumference is found from the equation 2 x Pi x R.  So to find the total surface area of a cylinder the equation is: (2 x Pi x R²) + (2 x Pi x R)

Online Calculator for Cylinder Surface Area
Online Calculator for Circle Circumference

Now you have the basic math behind the cylinder.  What other objects would you consider to be cylinders?  What is the surface area or volume of those objects?  I like to know the volume of the pizza I eat, try that next time you're at a restaurant.

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