# Cylinder

Go to Surface Area or Volume.

Cylinder Facts

Notice these interesting things:

• 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.

## Surface Area of a Cylinder

The Surface Area has these parts:

• Surface Area of Both Ends = 2 × π × r2
• Surface Area of Side = 2 × π × r × h

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:

• Area of the base: π × r2
• Height: h

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

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

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

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.