Answer
$\dfrac{35\sqrt 5 \pi }{3} $
Work Step by Step
The formula to determine the surface area is as follows:
$S= \int_{m}^{n} 2 \pi y \sqrt {1+(\dfrac{dy}{dx})^2} =\int_{0}^{15/4} 2 \pi [ 2 \sqrt {4-y} ] [\sqrt {\dfrac{5-y}{4-y} } dy$
Set $a^2=5-y$ and $ -dy =2u du$
Now$S=( -8\pi)\times \int_{\sqrt 5}^{\sqrt 5/2} a^2 da \\=(-8 \pi) \times [ \dfrac{ a^3}{3}]_{(\sqrt 5)}^{(\sqrt 5/2)}\\=\dfrac{35\sqrt 5 \pi }{3} $
