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Home » Case 1: All three numbers are even. - Simpleprint

Case 1: All three numbers are even. - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 s^3 = 100 \times 6\sqrt{2} = 600\sqrt{2}

📌 s = \sqrt[3]{600\sqrt{2}}

📌 s = (600\sqrt{2})^{1/3}

📌 Thus, the side length \( s \) is \(\boxed{(600\sqrt{2})^{1/3}}\).

📌 An AI model visualizes data clusters as spheres in 3D space. If the radius of a cluster sphere is reduced by 2 units, its volume decreases by \(128\pi\) cubic units. Find the original radius of the sphere.

📌 Let the original radius be \( r \). The volume of a sphere is:

📌 V = \frac{4}{3}\pi r^3

📌 After reducing the radius by 2, the new radius is \( r - 2 \), and the new volume is:

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