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

Let r and h be the radius and height of the cylinder, respectively.

Total surface of the cylinder = 2$\mathrm{\pi }$r(r + h)

Lateral surface area of the cylinder = 2$\mathrm{\pi }$rh

$\therefore \frac{\mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cylinder}}{\mathrm{Lateral}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cylinder}}$

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

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

So,

Total surface area of the cylinder : Lateral surface area of the cylinder = r + h : h

Thus, the ratio of the total surface area to the lateral surface area of a cylinder of base radius r and height h is r + h : h.

The ratio of the total surface area to the lateral surface area of a cylinder of base radius r and height h is ___r + h : h___.