The length of a road roller is 2.1m and its diameter is 1.4m. For levelling a ground 500 rotations of the road roller were required. How much area of ground was levelled by the road roller? Find the cost of levelling at the rate of Rs. 7 per sq. m.

#### Solution

Radius of the road roller, r = `1.4/2` = 0.7 m

Length of the road roller, h = 2.1 m

∴ Area levelled by the road roller in one rotation = Curved surface area of the road roller

= 2πrh

= 2 x `22/7` x 0.7 x 2.1

= 9.24 m^{2}

∴ Area of the ground levelled by the road roller = Area levelled by the road roller in 500 rotations

= 500 × Area levelled by the road roller in one rotation

= 500 × 9.24

= 4620 m^{2}

Rate of levelling the ground = Rs 7/m^{2}

∴ Cost of levelling the ground

= Area of the ground levelled by the road roller × Rate of levelling the ground

= 4620 × 7

= Rs 32,340

Thus, the area of ground levelled by the road roller is 4620 m^{2} and the cost of levelling the ground is Rs 32,340.