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Home » \(2^3 = 8 \equiv 3\) - Network4

\(2^3 = 8 \equiv 3\) - Network4

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 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:

📌 \frac{4}{3}\pi (3x)^3 = \frac{4}{3}\pi (27x^3) = 36\pi x^3

📌 Volume of the cylinder:

📌 \pi (2x)^2 (5x) = \pi (4x^2)(5x) = 20\pi x^3

📌 \frac{36\pi x^3}{20\pi x^3} = \frac{36}{20} = \frac{9}{5}

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