math zoom: cylinder facts

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

Surface Area = 2 × π × r × (r+h)

Which is made up of:

Surface Area of One End = π × r²
Surface Area of Side = 2 × π × 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

Volume = π × r²× h

Just multiply the area of the base by the height of the cylinder:

Area of the base: π × r²
Height: h
Volume = Area × Height = 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 equals 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:

The volume of a cylinder is:	π × r²× h
The volume of a cone is:	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.