Question

A road roller used for levelling a road of width 2m. It was observed that, the road roller required 25 complete revolutions to complete the levelling of road. If the diameter and length of roller is 7m and 2m respectively, then length of road is [use $\pi$ = 3.14].

• A. 1099 m
• B. 1999 m
• C. 1100 m
• D. 1234 m

Answer 1

The correct option is A

1099 m

Surface area of cylinder = 2$\pi$rh = 2$\pi$(7)(2) = 87.92 $m^2$.

Imagine a cloth used to cover a cylinder is unfold, what shape it appears to be, it would be a rectangle. So, each time the roller would revolve on the road it would cover an area of a rectangle exactly equal to the surface area of the cylinder.

So, as the roller revolves for 25 times it would cover an area of (25 × 87.92)$m^2$ = 2198 $m^2$.

This area would be equal to the area of the rectangle formed by the road i.e. 2198 = 'l' × 2. Hence 'l' = 1099m