Torus Volume Calculator

The Torus Volume Calculator is a tool designed to help you calculate the volume of a torus, a geometric shape resembling a doughnut. This calculator is useful for students, engineers, and math enthusiasts who need precise calculations for their projects or studies.

Data Source and Methodology

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da risorse matematiche autorevoli.

The Formula Explained

The volume of a torus is calculated using the formula:

\[ V = 2 \pi^2 R r^2 \]

Glossary of Variables

R: Large radius (distance from the center of the tube to the center of the torus).
r: Small radius (radius of the tube).
V: Volume of the torus.

How It Works: A Step-by-Step Example

Suppose R = 5 and r = 2. The volume of the torus would be calculated as follows:

\[ V = 2 \times \pi^2 \times 5 \times 2^2 = 2 \times \pi^2 \times 5 \times 4 = 40 \pi^2 \approx 394.78 \]

Frequently Asked Questions (FAQ)

What is a torus?

A torus is a 3D geometric shape resembling a doughnut, characterized by a larger outer radius and a smaller inner tube radius.

How do I calculate the volume of a torus?

You can calculate the volume using the formula V = 2π²Rr², where R is the large radius and r is the small radius.

What units should I use?

Ensure that the large and small radii are in the same units to get the volume in cubic units.

Can this calculator be used for other shapes?

This particular calculator is specifically designed for toroidal shapes.

Why is volume important?

Volume helps us understand the capacity or space occupied by a 3D object.