Cone

Go to Surface Area or Volume.

Cone Facts

Notice these interesting things:

cone shiny

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

cone apex and 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.

cone dimensions h=height, r=radius, s=side length

Surface Area of a Cone

The Surface Area has two parts:

Which together makes:

Surface Area = π × r × (r + s)

Note: we can calculate s = √(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)
 = 2π√(53)
 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

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

wooden cone narrowwooden cone mediumwooden cone wide

Construction Cone

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!