The diameter of a roller is 84 cm, and its length is 120 cm. It takes 500 complete revolutions to move once over and level a playground. What is the area of the playground in m²?

Diameter of the roller = 84 cm
Then radius is = 84 ÷ 2 = 42 cm
Length of the roller = 120 cm
Number of revolutions = 500

Step 1:Calculate the curved surface area of the roller

The formula for the curved surface area (CSA) of a cylinder is:
CSA = 2 × π × r × h
Where:
r = 42 cm (radius)
h = 120 cm (length)

Substitute the values:
CSA = 2 × (22/7) × 42 × 120
CSA = 2 × (22/7) × 5040
CSA = (2 × 22 × 5040) ÷ 7 = 31680 cm²

Step 2:Calculate the area of the playground

Each revolution of the roller covers an area equal to its curved surface area.
So, the area covered by 500 revolutions is:
Total area = 500 × 31680 cm² = 15840000 cm²

Convert the area from cm² to m² (since 1 m² = 10,000 cm²):
Total area = 15840000 ÷ 10000 = 1584 m²

Hence the area of the playground is 1584 m².