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Home » Choose the positive solution: \( n = rac2002 = 100 \). - Parker Core Knowledge

Choose the positive solution: \( n = rac2002 = 100 \). - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 A high school student is designing a garden with a circular pond and a semicircular walkway around it. If the radius of the pond is \(r\) units and the radius of the walkway is \(5r\) units, what is the ratio of the area of the pond to the area of the walkway?

📌 To find the ratio of the areas, we calculate the area of each shape.

📌 The area \(A\) of a circle with radius \(r\) is given by:

📌 A_{\text{pond}} = \pi r^2

📌 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

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