Question

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

• A. 1200 m
• B. 2100 m
• C. 1100 m
• D. 1234 m

Answer 1

The correct option is C

1100 m

Given, Radius of Cylinder, $r=7\text{m}$
length of roller, $h=2\text{m}$
Width of road, $B=2\text{m}$
Length of road be ${}^{\prime }{L}^{\prime }$
Number of revolution taken = 25

Roller rolls on its curved surface area.
$\therefore$ Surface area of = CSA of cylinder
one revolution
$=2\pi rh=2\times \frac{22}{7}\times 7\times 2=88{\text{m}}^2$

Total area covered in 25 revolution $=25\times 88=2200{\text{m}}^2$

This area will be equal to the area of the road levelled

$\text{Area of road =}L\times B=2200\Rightarrow L\times 2=2200\Rightarrow L=1100\text{m}$

$\therefore$ Length of the level road is 1100 m.