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 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)
Which is made up of:
- Surface Area of Base = π × r^{2}
- Surface Area of Side = π × r × s
- OR Surface Area of Side = π × r × √(r^{2}+h^{2})
Example: h = 7 and r = 2
Surface Area of Base | = π × r^{2} | |
= π × 2^{2} | ||
= 4π | ||
≈ 12.57 | ||
Surface Area of Side | = π × r × √(r^{2}+h^{2}) | |
= π × 2 × √(2^{2}+7^{2}) | ||
= π × 2 × √(4+49) | ||
= 2√(53) × π | ||
≈ 45.74 |
Total Surface Area ≈ 12.57 + 45.74 ≈ 58.31
Volume of a Cone
Volume = \frac{1}{3} π × r^{2 }× h
Example: h = 7 and r = 2
Volume | = \frac{1}{3} π × r^{2} ^{ }× h | |
= \frac{1}{3} π × 2^{2} ^{ }× 7 | ||
= \frac{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 × r^{2 }× h |
The volume of a cone is: | \frac{1}{3} π × r^{2 }× h |
So a cone's volume is exactly one third ( \frac{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
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!