# 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 × π2 × R × r

### Example: r = 3 and R = 7

 Surface Area = 4 × π2 × R × r = 4 × π2 × 7 × 3 = 4 × π2 × 21 = 84 × π2 ≈ 829

## Volume

Volume = 2 × π2 × R × r2

### Example: r = 3 and R = 7

 Volume = 2 × π2 × R × r2 = 2 × π2 × 7 × 32 = 2 × π2 × 7 × 9 = 126 π2 ≈ 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: