Question

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

Answer 1

Step: Find out the area of road.

Given,

Diameter of road roller, $d=84cm$

The radius of road roller,$r=\frac{d}{2}=\frac{84}{2}=42cm$

Length of road roller, $h=1m=100cm$.

We know that the formula for Curved surface area of road roller $=2\mathrm{\pi rh}$

$$\begin{gathered} =2\times \frac{22}{7}\times 42\times 100 \\ =26400 \end{gathered}$$

The curved surface area of the road roller is $26400c{m}^2$

Area covered by a road roller in $750$ revolutions$=26400\times 750$

$$\begin{gathered} =19800000c{m}^2 \\ =1980m^2\left[\because 1m^2=10000c{m}^2\right] \end{gathered}$$

Therefore, the area of the road is $1980m^2$.