# Cylinder

*Go to Surface Area or Volume.*

**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

A wooden cylinder

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

## Oblique Cylinder

When the two ends are directly aligned on each other it is a Right Cylinder otherwise it is an Oblique Cylinder:

## Surface Area of a Cylinder

The Surface Area has these parts:

*Surface Area of Both Ends*= 2 × π × r^{2}*Surface Area of Side*= 2 × π × r × h

Which together make:

Surface Area = 2 × π × r × (r+h)

### Example: h = 7 and r = 2

**113.097**

Try it yourself: cut some paper so it fits around a cylinder, then unwrap and measure it.

It will be **h** high and **2πr** (the circumference of a circle) long:

Side area = **2****π****rh**

Don't forget the two end bits:

Total
Surface Area

= 2(πr^{2}) + 2πrh

= 2πr(r+h)

## 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 × r
^{2} - Height: h

And we get:

Volume = π × r^{2 }× h

### Example: h = 7 and r = 2

^{2}× h

^{2}× 7

**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 **z ^{2}**, but you get the idea!)

Play with it here. The formula also works when it "leans over" (*oblique*) but remember that the height is always at right angles to the base:

And this is why:

The stack leans over, but still has the same volume

## Volume of a Tank

Learn how to find the volume of a partly filled horizontal cylinder like this one:

## Volume of a Cone vs Cylinder

The volume formulas for cylinders and cones are very similar:

Volume of a cylinder: | π × r^{2 }× h |

Volume of a cone: | \frac{1}{3} π × r^{2 }× h |

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

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

## Like a Prism

A cylinder is like a prism with an infinite number of sides, see Prism vs Cylinder.

## 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 shown above.

## More Cylinders

*"We eat what we can
And what we can't we can"*