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Home » I = 9\sqrt3 - 8 - Nurtured Nest

I = 9\sqrt3 - 8 - Nurtured Nest

📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 The area \(A\) of a semicircle with radius \(R\) is half the area of a circle:

📌 A_{\text{semicircle}} = \frac{1}{2} \pi R^2

📌 For the walkway with radius \(5r\):

📌 A_{\text{walkway}} = \frac{1}{2} \pi (5r)^2 = \frac{1}{2} \pi \times 25r^2 = \frac{25}{2} \pi r^2

📌 The area of the walkway is the area of the full circle with radius \(5r\) minus the area of the pond:

📌 A_{\text{walkway only}} = \pi (5r)^2 - \pi r^2 = 25\pi r^2 - \pi r^2 = 24\pi r^2

📌 The ratio of the area of the pond to the area of the walkway is:

📌 \text{Ratio} = \frac{A_{\text{pond}}}{A_{\text{walkway only}}} = \frac{\pi r^2}{24\pi r^2} = \frac{1}{24}

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