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Home » Thus, the sum of the roots is \(\boxed0\). - Midis

Thus, the sum of the roots is \(\boxed0\). - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 The volume \(V_{\text{sphere}}\) of a sphere with radius \(r\) is:

📌 V_{\text{sphere}} = \frac{4}{3}\pi r^3

📌 For the sphere with radius \(2x\):

📌 V_1 = \frac{4}{3}\pi (2x)^3 = \frac{4}{3}\pi (8x^3) = \frac{32}{3}\pi x^3

📌 The volume \(V_{\text{hemisphere}}\) of a hemisphere with radius \(r\) is half the volume of a full sphere:

📌 V_{\text{hemisphere}} = \frac{1}{2} \cdot \frac{4}{3}\pi r^3 = \frac{2}{3}\pi r^3

📌 For the hemisphere with radius \(3x\):

📌 V_2 = \frac{2}{3}\pi (3x)^3 = \frac{2}{3}\pi (27x^3) = 18\pi x^3

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