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Question
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 m2. How many revolutions did it make?
Solution
Given: length of cylindrical roller, i.e., height of the cylinder, h = 2.5 m
Radius of cylindrical roller, r = 1.75 m
The cylindrical roller will roll on the road only from its curved surface.
So, curved surface area of cylindrical roller, CSA = 2πrh
⇒ CSA = 2 × `22/7` × 1.75 × 2.5 = 27.5 m2
⇒ Area of road covered in 1 revolution = 27.5 m2
And given that, total area of road covered = 5500 m2
So, number of revolutions made by road roller to cover 5500 m2 = `5500/27.5` = 200
Thus, it made 200 revolutions.
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