Question

The surface area of the cone is 43.75pie cm^2. What is the slant height of the cone and the diameter is 5

Answer 1

If the diameter of the cone is 5, then the radius of it will be half that, or 2.5, thus

$\bf \textit{total surface area of a cone}\\\\ SA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ ------\\ SA=43.75\pi \\ r=2.5 \end{cases} \\\\\\ 43.75\pi =\pi (2.5)\sqrt{r^2+h^2}+\pi (2.5)^2 \\\\\\ 43.75\pi -\pi (2.5)^2=2.5\pi \sqrt{r^2+h^2} \\\\\\ 43.75\pi -6.25\pi =2.5\pi \sqrt{r^2+h^2}\implies 37.5\pi =2.5\pi \sqrt{r^2+h^2} \\\\\\ \cfrac{37.5\pi }{2.5\pi }=\sqrt{r^2+h^2}\implies 15=\sqrt{r^2+h^2}$