Question

the curved surface area of a cylinder (whose height is h and radius is r) is one third of its toal surface area. find h.

Answer 1

curved surface area = 1/3(total surface area)
$$\begin{gathered} 2\mathrm{\pi rh}=\frac{1}{3}(2{\mathrm{\pi r}}^2+2\mathrm{\pi rh}) \\ 6\mathrm{\pi rh}=2{\mathrm{\pi r}}^2+2\mathrm{\pi rh} \\ 4\mathrm{\pi rh}=2{\mathrm{\pi r}}^2 \\ 2\mathrm{h}=\mathrm{r} \\ \mathrm{h}=\frac{\mathrm{r}}{2} \end{gathered}$$