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?

Answer 1

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.