Question

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.

Answer 1

Radius of the road roller, r = $\frac{1.4}{2}$ = 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

= 2$\mathrm{\pi }$rh

= $2\times \frac{22}{7}\times 0.7\times 2.1$

= 9.24 m²

∴ 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 m²

Rate of levelling the ground = Rs 7/m²

∴ 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 m² and the cost of levelling the ground is Rs 32,340.