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
This ice cream cone is conical,
with spheres of ice cream on top
A Cone is a Rotated Triangle
A cone can be made by rotating a right-angled triangle.
The triangle is rotated around either of its two shorter sides which becomes the axis of the cone.
Right vs Oblique Cone
A right cone has its apex directly above the center of its circular base:
An oblique cone has its apex offset from the center,
giving it a slanted appearance.
Surface Area of a Cone
The Surface Area has two parts:
- The Base Area = π × r2
- The Side Area = π × r × s
Where r is the radius of the base, h is the cone's height and s is the slant length.
Which together makes:
Surface Area = π × r × (r + s)
The slant length can be calculated using Pythagoras:
s = √(r2 + h2)
Example: h = 7 and r = 2
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
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 × 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
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!