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energy drinks without taurine - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 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:

📌 V_{\text{new}} = \frac{4}{3}\pi (r - 2)^3

📌 The volume decrease is:

📌 \frac{4}{3}\pi r^3 - \frac{4}{3}\pi (r - 2)^3 = 128\pi

📌 Divide through by \( \frac{4}{3}\pi \):

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