Question

A road roller takes $750$ complete revolutions to move once over to level a road . Find the area of road if the diameter of a road roller is $84cm$ and length is $1m$ .

Answer 1

Area of road covered by roller $=750\times$ area covered in $1$ revolution.

$=750\times$ lateral surface area of cylinder.

$=750\times 2\pi rh$

So, Area of road $=750\times 2\pi rh$ ---(1)

it is given that, in cylinder

$d=84cm$

$\Rightarrow r=42cm$

$\Rightarrow r=\frac{42}{100}m$

Length of the roller $\left(h\right)=1m$

Now, from (1),

Area of road covered by roller,

$=750\times 2\pi rh$

$=750\times 2\times \frac{22}{7}\times \frac{42}{100}m\times 1m$

$=\frac{1500\times 132}{100}{m}^2$

$=1980m^2$

Therefore, area of road covered by roller is $1980m^2$.