Step 1:

The curve is $\"\"$ , $\"\"$ .

Definition of the surface area:

If the curve $\"\"$ , $\"\"$ is rotating about $\"\"$ -axis, then the area of the resulting surface area is given by,

$\"\"$ .

Here $\"\"$ and $\"\"$ .

Consider $\"\"$ .

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

$\"\"$

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

$\"\"$

Solution:

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