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
Surface Area = 2 × π × r × (r+h)
Which is made up of:
- Surface Area of One End = π × r^{2}
- 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 × r^{2 }× h
Just multiply the area of the base by the height of the cylinder:
- Area of the base: π × r^{2}
- Height: h
- Volume = Area × Height = π × r^{2 }× h
Example: h = 7 and r = 2
Volume | = π × r^{2} ^{ }× h | |
= π × 2^{2} ^{ }× 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 z^{2}, 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 × r^{2 }× h |
The volume of a cone is: | \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!
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.
More Cylinders