Question:
The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is
(a) 1 : 7
(b) 1 : 5
(c) 7 : 1
(d) 8 : 1
Solution:
$r=\frac{1.6 \mathrm{~m}}{2}$
$=\frac{160}{2}$
$=80 \mathrm{~cm}$
$h=20 \mathrm{~cm}$
The ratio of lateral surface to the total surface area of cylinder
$\frac{s_{1}}{s_{2}}=\frac{h}{(h+r)}$
$=\frac{20}{(20+80)}$
$\frac{s_{1}}{s_{2}}=\frac{20}{100}$
$=\frac{1}{5}$
$s_{1}: s_{2}=1: 5$
Hence, the correct answer is choice (b).
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