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Home » The ratio of the volume of the cone to the volume of the cylinder is: - SUpost

The ratio of the volume of the cone to the volume of the cylinder is: - SUpost

📅 July 7, 2026 👤 scraface

Jul 07, 2026

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📌 The corresponding \(y\)-coordinates are \(y = x + 2\), so:

📌 y = (-1 + \sqrt{7}) + 2 = 1 + \sqrt{7}, \quad y = (-1 - \sqrt{7}) + 2 = 1 - \sqrt{7}

📌 The points of intersection are \(A = (-1 + \sqrt{7}, 1 + \sqrt{7})\) and \(B = (-1 - \sqrt{7}, 1 - \sqrt{7})\).

📌 The area is the area of the circular segment. The central angle \( heta\) subtended by the chord can be found using the dot product of vectors from the origin to the points.

📌 Let \(ec{OA} = \langle -1 + \sqrt{7}, 1 + \sqrt{7}

📌 angle\), \(ec{OB} = \langle -1 - \sqrt{7}, 1 - \sqrt{7}

📌 Dot product:

📌 ec{OA} \cdot ec{OB} = (-1 + \sqrt{7})(-1 - \sqrt{7}) + (1 + \sqrt{7})(1 - \sqrt{7})

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