A cylindrical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 $m^2$. How many revolutions did it make?
Given:
Length of the roller $=2.5\ m$.
Radius of the roller$=1.75\ m$.
Area covered by the roller$=5500\ m^2$.
To do:
We have to find the number of revolutions taken by the roller.
Solution:
Area covered by cylindrical roller in one revolution $=$ Curved surface area of the cylinder
Curved surface of the cylindrical roller $=2πrh$
$=2\times\frac{22}{7}\times1.75\times2.5$
$=110\times0.25$
$=27.5\ m^2$
Number of revolutions taken by the cylinder$=\frac{Total\ area\ covered\ by\ the\ roller}{Curved\ surface\ of\ the\ cylindrical\ roller}$
$=\frac{5500}{27.5}$
$=200$
Number of revolutions made by the roller is 200.
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