What will be the ratio of the total surface area to the curved surface area of a cylinder with base radius 80 cm and height 20 cm?

Given, 

The base radius of the cylinder, r = 80 cm 

And the height of the cylinder, h = 20 cm 

We know that, 

The total surface area of cylinder = $2\pi r(r+h)$

And the curve surface area of cylinder = $2\pi rh$

Ratio of the total surface area to the curve surface area of a cylinder 

$=\frac{\mathrm{Total} \mathrm{surface} \mathrm{area} \mathrm{of} \mathrm{cylinder}}{\mathrm{Curve} \mathrm{surface} \mathrm{area} \mathrm{of} \mathrm{cylinder}}$

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

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

$=\frac{80+20}{20}$

$=\frac{100}{20}$

$=\frac{5}{1}$

$=5 :\hspace{0.17em}1$ 

Hence, the ratio of the total surface area to the curve surface area of a cylinder is 5 : 1.