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?

Question

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?

1. A. 139 m² (Correct answer)
2. B. 135 m²
3. C. 142 m²
4. D. 150 m²

Correct Answer

Option A — 139 m²

Detailed Solution & Explanation

The correct answer is 139 m².

Key Points

• A path around a circle forms an annulus, so its area is the outer circle minus the inner.
• Outer radius $= 14 + 1.5 = 15.5$ m.
• Area $= \pi(15.5^2 - 14^2) = \pi(240.25 - 196) = \pi \times 44.25 \approx$ 139 m².

Additional Information

• The difference of squares makes this quick: $15.5^2 - 14^2 = (15.5 + 14)(15.5 - 14) = 29.5 \times 1.5 = 44.25$.
• The path is built outside the park, so 1.5 m is added to the radius. Had it been inside, it would be subtracted.
• Using $\pi = 22/7$ gives $44.25 \times 22/7 = 139.07$, confirming the approximation.

प्रश्न (हिन्दी में)

एक वृत्ताकार पार्क की त्रिज्या 14 मीटर है। यदि इसके चारों ओर 1.5 मीटर चौड़ा पथ बनाया जाए, तो पथ का अनुमानित क्षेत्रफल क्या है?

1. A. 139 मीटर²
2. B. 135 मीटर²
3. C. 142 मीटर²
4. D. 150 मीटर²