$\"\"$

\

The equation of the curve is $\"\"$ .

\

Since the diameter of the dish is $\"\"$ , the radius of the dish is $\"\"$ .

\

Maximum length of the dish is $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in the above equation.

\

$\"\"$

\

The value of $\"\"$ is $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

Thus, the equation is $\"\"$ .

\

$\"\"$

\

The differential of arc length : $\"\"$ .

\

Consider $\"\"$ .

\

Differentite with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Surface area of the curve when rotated about $\"\"$ -axis : $\"\"$ .

\

Substitute $\"\"$ in the above formula.

\

$\"\"$

\

Let $\"\"$ .

\

$\"\"$

\

Substitute corresponding values in the above equation.

\

$\"\"$

\

Substitute $\"\"$ in the above equation.

\

$\"\"$

\

Therefore, the surface area of the dish is $\"\"$ .

\

$\"\"$

\

The value of $\"\"$ is $\"\"$ .

\

The surface area of the dish is $\"\"$ .