# Cone

Go to Surface Area or Volume.

Cone Facts

Notice these interesting things:

• It has a flat base
• It has one curved side
• It is not a polyhedron as it
has a curved surface

 The pointy end of a cone is called the vertex or 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 is made by rotating a triangle!

The triangle has to be 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.

## Surface Area of a Cone

Surface Area = π × r × (r + s)

• Surface Area of Base = π × r2
• Surface Area of Side = π × r × s
• OR Surface Area of Side = π × r × √(r2+h2)

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

 Surface Area of Base = π × r2 = π × 22 = 4π ≈ 12.57
 Surface Area of Side = π × r × √(r2+h2) = π × 2 × √(22+72) = π × 2 × √(4+49) = 2√(53) × π ≈ 45.74

Total Surface Area ≈ 12.57 + 45.74 ≈ 58.31

## Volume of a Cone

Volume = 1 3 π × r2 × h

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

 Volume = 1 3 π × r2 × h = 1 3 π × 22 × 7 = 28 3 π ≈ 29.32

## Volume of a Cone vs Cylinder

The volume formulas for cones and cylinders 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!