$\"\"$

\

The function is $\"\"$ .

\

$\"\"$

\

Consider $\"\"$ .

\

Differentiate on each side with respect to $\"\"$ .

\

$\"\"$

\

Graph the function $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

Region is bounded by graph on the interval $\"\"$ .

\

$\"\"$

\

Area of surface of revolution formed by revolving the graph of $\"\"$ about horizontal or vertical axis is \ \

\

$\"\"$ .

\

Where $\"\"$ is continuous function on interval $\"\"$ and $\"\"$ is the distance between thegraph of $\"\"$ and axis of revolution.

\

Calculate area of the upper half and then by symmetry multiply the result by 2.

\

Substitute corresponding values.

\

Therefore, $\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

There is an infinite discontinuity at $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Total surface area is double the upper half.

\

$\"\"$ square units.

\

$\"\"$

\

Surface area of revolution of torus is $\"\"$ square units.