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But we need dV/dt at this instant: - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 An urban planner is designing a circular roundabout with a radius of 10 meters, surrounded by a circular path that is 2 meters wide. What is the area of the path alone in square meters?

📌 First, find the area of the larger circle, which includes both the roundabout and the path. The radius of this larger circle is \(10 + 2 = 12\) meters.

📌 The area \( A_{\text{large}} \) of the larger circle is:

📌 A_{\text{large}} = \pi (12)^2 = 144\pi

📌 Next, find the area of the smaller circle (the roundabout), which has a radius of 10 meters:

📌 A_{\text{small}} = \pi (10)^2 = 100\pi

📌 The area of the path is the difference between the area of the larger circle and the smaller circle:

📌 A_{\text{path}} = A_{\text{large}} - A_{\text{small}} = 144\pi - 100\pi = 44\pi

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