Learn How to Calculate Torus Volume, Surface Area Using Inner, Outer Radius - Tutorial

How to Calculate Volume and Surface Area of Torus - Definition, Formula and Example

Definition

Torus is a ring-shaped surface of revolution created by rotating a circle in three-dimensional space about an axis coplanar with the circle that does not intersect the circle.

Formula

torus Surface Area = π2(R2 - r2) Volume = π2(R + r)(R - r)2 / 4
Where,
R = Outer Radius r = Inner Radius

Example

In a ring-shaped object the outer radius is 20 and inner radius is 10. Find the surface area and volume of that object.

Given,

Outer Radius = 20 Inner Radius = 10

To Find,

Surface area and Volume of Torus

Solution :
Step 1 :

Let us first calculate the surface area for the object, Substitute the values in the below formula, Surface Area= π2(R2 - r2) = π2 (20 x 20 - 10 x 10) = π2 (400 - 100) = π2 x 300 = 2960.8813

Step 2 :

Now, let us calculate the volume of torus, Volume= π2(R + r)(R - r)2 / 4 = π2 (20 + 10) (20 - 10)2 / 4 = (π2 x 30 x 10 x 10) / 4 = (π2 x 3000) / 4 = 29608.8132 / 4 = 7402.2033 Hence the surface area and volume of torus is calculated.

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