A circular park having a radius of 14 m. If a 1.5 m wide path is built around it, what is the approximate area of the path?

Correct — A. The path is the ring between the park and a larger circle around it.

Inner radius r = 14 m
Outer radius R = 14 + 1.5 = 15.5 m

Path area = π(R² − r²) = π(15.5² − 14²)
= π(240.25 − 196) = π × 44.25
= 22⁄7 × 44.25 ≈ 139.07
≈ 139 m² → option (a)

Why the others are wrong

• (b)
  135 m² — 135 m² would need R² − r² ≈ 43. The ring here has 15.5² − 14² = 44.25, which gives 139 m² with π = 22⁄7 or 3.14.
• (c)
  142 m² — 142 m² would need R² − r² ≈ 45.2 (142 × 7⁄22). The true figure is 44.25, so the area is about 139 m².
• (d)
  150 m² — 150 m² overshoots by about 11 m². It would need R² − r² ≈ 47.7, but 15.5² − 14² is 44.25.

A path of width w around a circle of radius r makes an outer circle of radius r + w. The path is the ring between them: area = π(R² − r²).

Factorising saves squaring: R² − r² = (R − r)(R + r) = 1.5 × 29.5 = 44.25.

The same area is the mean circumference × width: 2π × 14.75 × 1.5 ≈ 139.07 m².

Key facts

• Outer radius = inner radius + path width: 14 + 1.5 = 15.5 m.
• Ring area = π(R² − r²) = π(R − r)(R + r).
• Here π × 44.25 ≈ 139.07 m² with π = 22⁄7.

Common traps

• Adding the width twice to the radius (14 + 3 = 17 m), which gives π(17² − 14²) ≈ 292 m². The diameter grows by 3 m, the radius by 1.5 m.
• Multiplying the park's circumference by the width, 2π × 14 × 1.5 = 132 m², which misses the longer outer edge.

No directly related past PYQ was found.