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ight) = 12 imes rac12 imes rac23 = 4. - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \pi (5)^2 = 25\pi \text{ μm}^2

📌 The square is inscribed in the circle, so its diagonal is the diameter, 10 μm. For a square, diagonal $ d = s\sqrt{2} $, so:

📌 s = \frac{10}{\sqrt{2}} = 5\sqrt{2} \text{ μm}

📌 The area outside the square but inside the circle is:

📌 25\pi - 50 = 25(\pi - 2) \text{ μm}^2

📌 Thus, the region's area is $ \boxed{25(\pi - 2)} $.

📌 Question: A sustainable energy facility uses a cylindrical battery casing with radius $ 2x $ and height $ 5x $. A spherical capacitor of radius $ 3x $ is placed inside. What is the ratio of the volume of the spherical capacitor to the volume of the cylindrical casing?

📌 Solution: Volume of the sphere:

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