A circular park of radius 21 m has a path 3.5 m wide all around it, outside. Find the area of the path and the cost of tiling it at an example rate of ₹ 20 per m². (Use π = 22/7)

1. 1 · Write what is given and what is to be found Given: inner radius r = 21 m, path width 3.5 m, rate ₹ 20 per m². To find: area of the path and the cost.
2. 2 · Draw the figure Two circles with the same centre O: inner radius 21 m, outer radius 24.5 m. Shade the ring between them.
3. 3 · Write the formula or theorem Area of a ring = π(R² − r²) = π(R − r)(R + r).
4. 4 · Find the outer radius R = 21 + 3.5 = 24.5 m.
5. 5 · Find the area Area = (22/7) × 3.5 × 45.5 = 11 × 45.5 = 500.5 m².
6. 6 · Find the cost Cost = 500.5 × 20 = ₹ 10,010.
7. 7 · Check and box the answer Area of the path = 500.5 m²; cost = ₹ 10,010 at the example rate.

Scoring tip: Factorise R² − r² as (R − r)(R + r). It turns a hard square into an easy multiplication.