Explanation

(b)
$Curved\ surface = \int_{a}^{b}{2\ \ \pi y\sqrt{\left\lbrack 1 + \left( \frac{dy}{dx} \right)^{2} \right\rbrack}dx}$
$Given\ that,\ a = 2b = 3\ and\ y = x + 1$
$\therefore\frac{dy}{dx} = 1 + 0 \Longrightarrow \frac{dy}{dx} = 1$
Therefore, curved surface
$= \int_{2}^{3}{2\pi(x + 1)\sqrt{\left\lbrack 1 + (1)^{2} \right\rbrack}dx = 2\sqrt{2}\ \ \pi\int_{2}^{3}{(x + 1)dx}}$
$= 2\sqrt{2}\pi\left\lbrack \frac{(x + {1)}^{2}}{2} \right\rbrack_{2}^{3} = \sqrt{2}\pi(16 - 9) = 7\pi\sqrt{2}$