Parabola passes through the points (9,4) and (-9,4).
[tex]y=ax^2
\\4=a(-9)^2
\\
\\a= \frac{4}{81}
\\
\\y=\frac{4}{81} x^2
[/tex]
The surface area of a paraboloid, not inculding its base
[tex]SA = \frac{\pi}{6}\frac{r}{h^2}[{(r^2 + 4h^2)}^{\frac{3}{2}} - r^3][/tex]
[tex]r=9,h=4
\\SA = \frac{\pi}{6}\frac{9}{4^2}[{(9^2 + 4\times4^2)}^{\frac{3}{2}} - 9^3]\approx 299.54[/tex]
