Cone

Go to Surface Area or Volume.

Cone Facts

Notice these interesting things:

cone shiny

  • 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

cone apex and 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:

right vs oblique cone

Surface Area of a Cone

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

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

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

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.

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

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!