Answer
$\dfrac{76 \pi}{3}$
Work Step by Step
We are given that $x=t^2/2 \implies \dfrac{dx}{dt}= t$ and $y=2t \implies \dfrac{dy}{dt}= 2$
The surface area is given as follows:
$S=\int_0^{\sqrt 5} 2\pi (2t) \sqrt {t^2+4} dt$
Plug in $t^2+4=a \implies da=2t$
Then, $S=\int_4^{9} 2\pi (a)^{1/2} da=2\pi [\dfrac{2}{3} a^{3/2}]+4^{9}$
Thus, $S=\dfrac{76 \pi}{3}$
