Answer
$$S = 27\sqrt {10} \pi $$
Work Step by Step
$$\eqalign{
& y = 3x,{\text{ }}0 \leqslant x \leqslant 3 \cr
& {\text{Differentiate}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {3x} \right] \cr
& \frac{{dy}}{{dx}} = 3 \cr
& {\text{Formula for surface area}} \cr
& S = 2\pi \int_a^b {r\left( x \right)\sqrt {1 + {{\left[ {f'\left( x \right)} \right]}^2}} } dx,{\text{ }}r\left( x \right) = f\left( x \right) \cr
& {\text{Then,}} \cr
& S = 2\pi \int_0^3 {\left( {3x} \right)\sqrt {1 + {{\left( 3 \right)}^2}} } dx \cr
& S = 6\sqrt {10} \pi \int_0^3 x dx \cr
& {\text{Integrate}} \cr
& S = 6\sqrt {10} \pi \left[ {\frac{{{x^2}}}{2}} \right]_0^3 \cr
& S = 6\sqrt {10} \pi \left[ {{x^2}} \right]_0^3 \cr
& S = 3\sqrt {10} \pi \left( {9 - 0} \right) \cr
& S = 27\sqrt {10} \pi \cr} $$
