Step 1:

The Parametric equations are $\"\"$ and $\"\"$ , $\"\"$ .

Definition of the surface area:

If the curve given by the parametric equations $\"\"$ and $\"\"$ , $\"\"$ is rotated about $\"\"$ -axis, then the area of the resulting surface is given by

$\"\"$

Consider $\"\"$ .

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

$\"\"$

Consider $\"\"$ .

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

$\"\"$

Step 2:

Substitute $\"\"$ , $\"\"$ and $\"\"$ in surface area formula.

$\"\"$

by using calculator,

$\"\"$

Solution:

$\"\"$