$\"\"$

The torus can be obtained by rotating $\"\"$ about the $\"\"$ -axis.

Consider the area swept out by the circle when rotated through a small angle $\"\"$ .

Take a point on the circle such that the radius to this point an angle $\"\"$ with radius towards the origin.

The distance of this point from the $\"\"$ -axis is $\"\"$ .

The rotation of the circle through $\"\"$ this point moves through a distance $\"\"$ .

The length of the arc generated by a rotation $\"\"$ is $\"\"$ .

Surface area of the torus is $\"\"$ . \ \

$\"\"$ .

Area is $\"\"$

$\"\"$

$\"\"$ .

$\"\"$

$\"\"$ .