Question

The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is
(a) 2 : 1
(b) 3 : 1
(c) 4 : 1
(d) 5 : 1

Answer 1

(d) 5 : 1
Ratio of the total surface area to the lateral surface area$=\frac{\text{Total surface area}}{\text{Lateral surface area}}$
$$\begin{gathered} =\frac{2\mathrm{\pi }r\left(h+r\right)}{2\mathrm{\pi }rh} \\ =\frac{h+r}{h} \\ =\frac{\left(20+80\right)}{20} \\ =\frac{100}{20} \\ =\frac{5}{1} \\ =5:1 \end{gathered}$$
Hence, the required ratio is 5:1.