# Cone

*Go to Surface Area or Volume.*

Cone Facts

**Notice these interesting things:**

- It has a circle at one end
- And a point at the other end
- And a curved side
- It is
**not**a polyhedron as it has a curved surface

- The pointy end of a cone is called the
**apex** - The flat part is the
**base**

An object shaped like a cone is said to be **conical**

## A Cone is a Rotated Triangle

A cone can be made by rotating a triangle!

The triangle is a right-angled triangle, and it gets rotated around one of its two short sides.

The side it rotates around is the **axis** of the cone.

## Right vs Oblique Cone

When the apex is aligned on the center of the base it is a Right Cone otherwise it is an Oblique Cone:

## Surface Area of a Cone

The Surface Area has two parts:

- The
*Base Area*= π × r^{2} - The
*Side Area*= π × r × s

Which together makes:

Surface Area = π × r × (r + s)

Note: we can calculate**s = √(r**

^{2}+h^{2})### Example: h = 7 and r = 2

^{2}

^{2}

**12.57**

^{2}+h

^{2})

^{2}+7

^{2})

**45.74**

Total Surface Area ≈ 12.57 + 45.74 ≈ **58.31**

## Volume of a Cone

Volume = \frac{1}{3} π × r^{2 }× h

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

^{2}

^{ }× h

^{2}

^{ }× 7

**29.32**

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:

## Volume of a Cone vs Cylinder

The volume formulas for cones and cylinders 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.

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

## Like a Pyramid

A cone is also like a pyramid with an infinite number of sides, see Pyramid vs Cone.

## Different Shaped Cones

## Construction Cone

This is * almost* a cone, but the top is chopped off (called a "truncated cone").

Also it has a wider base added so it doesn't fall over!