$\"\"$

\

A torus is formed by revolving the region bounded by the circle $\"\"$ .

\

Here the rotation is about the line $\"\"$ .

\

The distance from the center of the rectangle to the axis of revolution is $\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$

\

The height of the rectangle is $\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Find $\"\"$ .

\

Apply the integral formula: $\"\"$ . $\"\"$

\

$\"\"$ .

\

Find $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute corresponding values in the value.

\

$\"\"$

\

Above result is the volume of the top half of torus.

\

Total volume of the torus is $\"\"$ cubic units.

\

$\"\"$

\

Total volume of the torus is $\"\"$ cubic units.