A circular pond is surrounded by a path 2 m wide. If the total area (pond + path) is 616 m² and the pond area is 452.16 m², what…

Question

A circular pond is surrounded by a path 2 m wide. If the total area (pond + path) is 616 m² and the pond area is 452.16 m², what is the radius of the pond?

1. A. 10 m
2. B. 11 m
3. C. 12 m (Correct answer)
4. D. 13 m

Correct Answer

Option C — 12 m

Detailed Solution & Explanation

The correct answer is 12 m.

Key Points

• The total area covers pond plus path, so it gives the outer radius:
  • πR² = 616 → R² = 616 × 7/22 = 196 → R = 14 m
• The path is 2 m wide, so the pond's radius is 14 − 2 = 12 m.
• Check against the stated pond area: π × 12² = (22/7) × 144 ≈ 452.57, matching the given 452.16 to rounding.

Additional Information

• A total area of 616 is chosen deliberately: 616 × 7/22 = 196 is a perfect square, signalling that π = 22/7 should be used rather than 3.14.
• The width of a surrounding path is always the difference of the radii, so R = r + width — a relation that also gives the path's area as π(R² − r²).
• Areas worth recognising with π = 22/7: r = 7 → 154, r = 14 → 616, r = 21 → 1,386, r = 28 → 2,464.

प्रश्न (हिन्दी में)

एक गोलाकार तालाब 2 मीटर चौड़े रास्ते से घिरा हुआ है। यदि कुल क्षेत्रफल (तालाब + रास्ता) 616 वर्ग मीटर है और तालाब का क्षेत्रफल 452.16 वर्ग मीटर है, तो तालाब की त्रिज्या क्या है?

1. A. 10 मी
2. B. 11 मी
3. C. 12 मी
4. D. 13 मी