Question

The ratio of the total surface area to the lateral surface area of a cylinder of base radius r and height (h) is ______

Answer 1

Given:
The base radius and the height of the cylinder are $r$ and $h$ respectively.

Now, the total surface area
$=2\pi rh+2\pi r^2$ and the lateral surface area $=2\pi rh$

Required ratio
$=\frac{2\pi rh+2\pi r^2}{2\pi rh}$

$=\frac{2\pi r(r+h)}{2\pi rh}$

$=\frac{h+r}{h}=1+\frac{r}{h}$

Hence, the required ratio is
$1+\frac{r}{h}$