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A roller has a diameter of 0.5 m and a length of 1.5 m. Find the number of revolutions to cover the area of 264 sq.m.
Given :
The diameter of the roller(d) $=0.5 m$.
The length of the roller(h) $=1.5 m$.
To do :
We have to find the number of revolutions by the roller to cover the area of 264 sq m.
Solution :
Radius $= \frac{d}{2} = \frac{0.5}{2}$
Area covered by the roller in one revolution $=$ Curved surface area of the roller.
The curved surface area of the roller $= 2πrh$
$= 2 \times \frac{22}{7} \times \frac{0.5}{2} \times 1.5$
$= 2 \times \frac{22}{7} \times \frac{1}{2 \times 2} \times \frac{3}{2}$ $[0.5 =\frac{1}{2} ; 1.5 =\frac{3}{2} ]$
$ = \frac{33}{14}$sq m.
Area covered by the roller in one revolution $= \frac{33}{14}$sq m.
Number of revolutions $=$ Total area $\div$ Area covered in one revolution
$= \frac{264}{\frac{33}{14}}$
$= \frac{264 \times 14}{33}$
$ =8 \times 14 = 112$
Therefore, the number of revolutions is 112.
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