Cylinder

Go to Surface Area or Volume.

Cylinder Facts

Notice these interesting things:

cylinder shiny

  • It has a flat base and a
    flat top
  • The base is the same as the top
  • From base to top the shape stays the same
  • It has one curved side
  • It is not a polyhedron as it has a curved surface

An object shaped like a cylinder is said to be cylindrical.

 

Cylinder Dimensions: r=radius, h=height

Surface Area of a Cylinder

The Surface Area has these parts:

Which together make:

Surface Area = 2 × π × r × (r+h)

Example: h = 7 and r = 2

Surface Area = 2 × π × r × (r+h)
 = 2 × π × 2 × (2+7)
 = 2 × π × 2 × 9
 = 36 π
 113.097

Volume of a Cylinder

To calculate the volume we multiply the area of the base by the height of the cylinder:

And we get:

Volume = π × r2 × h

Example: h = 7 and r = 2

Volume= π × r2 × h
 = π × 22 × 7
 = 28 π
   87.96

How to remember: Volume = pizza

Cylinder Pizza

Imagine you just cooked a pizza.

The radius is "z", and the thickness "a" is the same everywhere ... what is the volume?

Volume =   pi × z × z × a

(we would normally write "pi" as π, and z × z as z2, but you get the idea!)

Volume of a Cone vs Cylinder

cone vs cylinder

 

The volume formulas for cylinders and cones are very similar:

Volume of a cylinder:   π × r2 × h
Volume of a cone:   1 3 π × r2 × h

So a cone's volume is exactly one third ( 1 3 ) of a cylinder's volume.

In future, order your ice creams in cylinders, not cones, you get 3 times as much!

It Doesn't Have to Be Circular

wooden elliptical cylinder

Usually when we say Cylinder we mean a Circular Cylinder, but you can also have Elliptical Cylinders, like this one:

And we can have stranger cylinders!

So long as the cross-section is curved and is the same from one end to the other, then it is a cylinder. But the area and volume calculations will be different than for the above.

More Cylinders

wooden cylinder tallwooden cylinder shortwooden cylinder thin