Problem

A curve has equation

$$y = \sqrt{9 - x^2} \qquad 0 \le x \le 3.$$

(a) Using calculus, show that the length of the curve is

$$\frac{3\pi}{2}.$$

The curve is rotated through $2\pi$ radians about the $x$-axis.

(b) Using calculus, find the exact area of the surface generated.