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Home » x + y = a \quad \textو \quad y + z = a - SUpost

x + y = a \quad \textو \quad y + z = a - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 The volume \(V\) of a cone with radius \(r\) and height \(h\) is given by the formula:

📌 V_{\text{cone}} = \frac{1}{3} \pi r^2 h

📌 Substituting \(r = 3y\) and \(h = 4y\), we get:

📌 V_{\text{cone}} = \frac{1}{3} \pi (3y)^2 (4y) = \frac{1}{3} \pi \cdot 9y^2 \cdot 4y = \frac{1}{3} \pi \cdot 36y^3 = 12\pi y^3

📌 The volume \(V\) of a sphere with radius \(r\) is given by:

📌 Substituting \(r = 2y\), we find:

📌 V_{\text{sphere}} = \frac{4}{3} \pi (2y)^3 = \frac{4}{3} \pi \cdot 8y^3 = \frac{32}{3} \pi y^3

📌 Now, compute the ratio of the volume of the cone to the volume of the sphere:

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