If the diameter and length of the drum of a road roller are 4.6 ft and 5.6 ft respectively, then how much area will be covered by the roller in 7 revolutions?

Diameter of the drum of the road roller = 4.6 ft

∴ Radius of the drum of the road roller = $\frac{1}{2}$× 4.6 ft = 2.3 ft

Length of the drum of the road roller = 5.6 ft

It is known that the lateral surface area of a cylinder is given by 2πrh, where r and h are the radius and height of the cylinder respectively.

⇒ Lateral surface area of the drum of the road roller $=2\times \frac{22}{7}\times 2.3\times 5.6$ = 80.96 ft²

∴ In one revolution, the drum of the road roller covers an area of 80.96 ft²

⇒ Area covered in 7 revolutions = (80.96 × 7) ft² = 566.72 ft²

Thus, the drum of the road roller covers an area of 566.72 ft² in 7 revolutions.