The diameter and the length of the drum of a road roller are 140 cm and 2 m respectively. How many rotations does it take to cover 2200 m² on the road?

The diameter of the cylindrical roller is 140 cm.

∴ Radius of the roller, $r=\frac{140}{2} cm$= 70 cm

Length of the roller, l = 2 m = 200 cm

The area covered by the roller in 1 revolution is equal to its curved surface area.

∴ 2πrh = $2\times \frac{22}{7}\times 70\times 200=88000 {\mathrm{cm}}^2=8.8 {\mathrm{m}}^2$ 

No. of rotations made by the roller $=\frac{\mathrm{Area} \mathrm{covered} \mathrm{by} \mathrm{the} \mathrm{roller} \mathrm{on} \mathrm{the} \mathrm{ground}}{\mathrm{Curved} \mathrm{surface} \mathrm{area} \mathrm{of} \mathrm{the} \mathrm{roller}}$

$=\frac{2200}{8.8}=250$ 

Thus, the drum of the road roller will take 250 rotations to cover 2200 m² on the road.