if the diameter of the cone is 5, then the radius of it will be half that, or 2.5, thus
[tex]\bf \textit{total surface area of a cone}\\\\
SA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}+\pi r^2~~
\begin{cases}
r=radius\\
h=height\\
------\\
SA=43.75\pi \\
r=2.5
\end{cases}
\\\\\\
43.75\pi =\pi (2.5)\sqrt{r^2+h^2}+\pi (2.5)^2
\\\\\\
43.75\pi -\pi (2.5)^2=2.5\pi \sqrt{r^2+h^2}
\\\\\\
43.75\pi -6.25\pi =2.5\pi \sqrt{r^2+h^2}\implies 37.5\pi =2.5\pi \sqrt{r^2+h^2}
\\\\\\
\cfrac{37.5\pi }{2.5\pi }=\sqrt{r^2+h^2}\implies 15=\sqrt{r^2+h^2}[/tex]
