The road roller is cylindrical in shape. The diameter d is 84 cm, so its radius r is 42 cm. Converting the radius to meters gives 0.42 m, while the length (height h) of the roller is 1 m.

a road roller takes and 50 complete revolutions to move once over to level a road find the area of the road if the diameter of the road roller is 84 cm and length is 1 m

Answer: 1980 m²

Step-by-step solution

Step 1: Identify the dimensions of the road roller

The road roller is cylindrical in shape. The diameter $d$ is $84\text{ cm}$ , so its radius $r$ is $42\text{ cm}$ . Converting the radius to meters gives $0.42\text{ m}$ , while the length (height $h$ ) of the roller is $1\text{ m}$ .

Step 2: Calculate the area covered in one revolution

In 1 complete revolution, the road roller covers an area equal to its curved surface area, given by $2\pi r h$ . Substituting $r = 0.42\text{ m}$ and $h = 1\text{ m}$ gives $2.64\text{ m}^2$ .

Step 3: Calculate the total area of the road

To find the total area of the road, multiply the area leveled in 1 revolution by the total number of revolutions, which is 750. This gives $750 \times 2.64 = 1980\text{ m}^2$ .

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