The radius of a garden roller is 1.8 m and it is 4 m long. How much area will…

Concept: The curved (lateral) surface area of a right circular cylinder of radius r and length l is 2πrl. A cylindrical roller making one complete revolution marks out ground equal to exactly this curved surface area; over n revolutions, the total ground area covered is n times this curved surface area.

1. Given: radius of the roller, r = 1.8 m; length of the roller, l = 4 m; number of revolutions, n = 10; use π = 22/7.

2. Curved surface area covered in one revolution = 2πrl = 2 × (22/7) × 1.8 × 4 = 316.8/7 m2.

3. = 45.25 m2 (to 2 decimal places), the curved surface area for one revolution.

4. Area covered in 10 revolutions = 10 × 45.25 m2 = 452.5 m2.

Cross-check: The area covered scales linearly with the number of revolutions, so dividing the total, 452.5 m2, by 10 revolutions returns 45.25 m2 per revolution -- matching the one-revolution curved surface area computed above, which confirms the total.

∴ The garden roller covers 452.5 m2 of ground in 10 revolutions.