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

 

 

brass cone
  • 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
cone vertex and base

 

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)

Which is made up of:

  • 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!

Different Shaped Cones