Final answer:
To find the area covered by the roller after 10 revolutions, use the formula A = 2πr × length for one revolution and multiply by the number of revolutions. With a roller of radius 0.7 meters and length 2 meters, the total area covered in 10 revolutions is 88 square meters.
Step-by-step explanation:
To find the area covered by the roller after 10 revolutions, we can calculate the surface area of the cylinder that the roller would have swept through its movement. This includes both the length of the roller and the circumference of its circular ends as it rotates. The formula to calculate the area covered (A) in one revolution for a cylindrical object is A = 2πr × length, where r is the radius of the cylindrical object and π (pi) is approximately 3.1415927. To find the total area covered in 10 revolutions, we simply multiply by 10.
With the radius (r) of the roller being 0.7 meters and the length (l) being 2 meters, the area covered in one revolution is A = 2π(0.7 m)(2 m). Plugging in the values, we get A = 2×3.1415927×0.7 m×2 m = 8.8 m² for one revolution. For 10 revolutions, the area covered would be 10 × 8.8 m² = 88 m². Therefore, the correct answer is 88 square meters.