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}{√(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)√(r^2+h^2)+\pi (2.5)^2 \\\\\\ 43.75\pi -\pi (2.5)^2=2.5\pi √(r^2+h^2) \\\\\\ 43.75\pi -6.25\pi =2.5\pi √(r^2+h^2)\implies 37.5\pi =2.5\pi √(r^2+h^2) \\\\\\ \cfrac{37.5\pi }{2.5\pi }=√(r^2+h^2)\implies 15=√(r^2+h^2)`