Torus
Go to Surface Area or Volume.
Torus Facts
Notice these interesting things:
- It can be made by revolving a
small circle (radius r) along a line made
by a bigger circle (radius R). - It has no edges or vertices
- It is not a polyhedron
Torus in the Sky.
The Torus is such a beautiful solid,
this one would be fun at the beach !
Surface Area
Surface Area = 4 × π^{2} × R × r
Example: r = 3 and R = 7
Surface Area | = 4 × π^{2} × R × r | |
= 4 × π^{2} × 7 × 3 | ||
= 4 × π^{2} × 21 | ||
= 84 × π^{2} | ||
≈ 829 |
Volume
Volume = 2 × π^{2} × R × r^{2}
Example: r = 3 and R = 7
Volume | = 2 × π^{2} × R × r^{2} | |
= 2 × π^{2} × 7 × 3^{2} | ||
= 2 × π^{2} × 7 × 9^{} | ||
= 126 π^{2} | ||
≈ 1244 |
Note: Area and volume formulas only work when the torus has a hole!
And did you know that Torus was the Latin word for a cushion?
(This is not a real roman cushion, just an illustration I made)
When we have more than one torus they are called tori
More Torus Images
As the small radius (r) gets larger and larger, the torus goes from looking like a Tire to a Donut: