the radius and height of a cylindrical box without lid are r and h respectively what is the total outer surface area of the box ?

Dear Student,          

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{We} \mathrm{have} : \\ \mathrm{r} = \mathrm{radius} \mathrm{of} \mathrm{base} \\ \mathrm{h} = \mathrm{height} \mathrm{of} \mathrm{cylinder} \\ \mathrm{Now}, \mathrm{outer} \mathrm{surface} \mathrm{area} \mathrm{of} \mathrm{open} \mathrm{cylindrical} \mathrm{box} = \mathrm{area} \mathrm{of} \mathrm{circular} \mathrm{base} + \mathrm{CSA} \\ \mathrm{outer} \mathrm{surface} \mathrm{area} \mathrm{of} \mathrm{open} \mathrm{cylindrical} \mathrm{box} = {\mathrm{\pi r}}^2 + 2\mathrm{\pi rh} = \mathrm{\pi r}\left[\mathrm{r}+2\mathrm{h}\right] \end{gathered}$$

Hope this would clear your doubt.                                                                 

Do let us know in case of any further concerns.                                                                 

Regards