Toroid facts for kids

A toroid made by spinning a square.

A torus looks like a doughnut.

In math, a toroid is a special kind of 3D shape. Imagine you have a flat shape, like a square or a circle. If you spin that shape around a central line (called an axis of revolution), and the line doesn't touch the shape itself, you create a toroid! It always has a hole in the middle, just like a ring.

For example, if you spin a rectangle, you get a hollow ring with a square-shaped cross-section. If you spin a circle, the shape you get is called a torus. A torus looks exactly like a doughnut!

Sometimes, the word toroid is also used for shapes that are like a doughnut but might not be perfectly round. These shapes can have more than one hole. Think of a pretzel – it has several holes!

What Makes a Toroid?

A toroid is created by taking a flat 2D shape and spinning it around a line. This line is called the "axis of revolution." The important thing is that this line must pass through the hole of the toroid and not touch the surface of the shape itself. This is what gives toroids their unique ring-like appearance.

For example, if you take a flat circle and spin it around an axis that is outside the circle, you get a perfect torus. This is the most common type of toroid.

Toroids in Real Life

You might not realize it, but toroid shapes are all around us! They appear in nature and in things we build.

• Doughnuts: This is the most famous example! A doughnut is a solid torus. It's made by spinning a disk (a solid circle) around an axis.
• Inner Tubes: The rubber rings used for swimming or floating are toroid shapes.
• Electronic Parts: In electronics, you'll find "toroidal inductors" and "toroidal transformers." These are wires wound around a doughnut-shaped core. They are very efficient at storing energy.
• Propellers: Some new types of propellers, like those used on drones, are designed with a toroid shape. This can make them quieter and more efficient.

Measuring Toroids

Even though the math can get tricky, we can still measure toroids. We can figure out their volume (how much space they take up) and their surface area (the total area of their outside).

To do this, we need to know the size of the flat shape that was spun and the distance from the center of that shape to the spinning axis.

Square Toroids

If you spin a square to make a toroid, its volume and surface area can be calculated. You need to know the side length of the square and the radius of the big circle that the square spins around.

Circular Toroids

For a circular toroid (a torus), the calculations are based on two main measurements:

• r: The radius of the small circle that was spun.
• R: The radius of the overall shape, measured from the very center of the doughnut to the center of the small circle.

Using these measurements, mathematicians have special formulas to find the volume and surface area of a torus.

See also

• Toroidal inductors and transformers
• Toroidal propellers
• Annulus
• Solenoid
• Helix
• In Spanish: Toroide para niños