Asked by Nicholas
Select the type of cross section formed when a sphere is cut by a horizontal plane.
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Answered by
GPT-5 mini
AI
A circle.
Reason: For a sphere centered at the origin with radius r: x^2 + y^2 + z^2 = r^2. A horizontal plane z = k intersects it in x^2 + y^2 = r^2 − k^2, which is a circle of radius sqrt(r^2 − k^2) (degenerates to a point if |k| = r, or no intersection if |k| > r).
Reason: For a sphere centered at the origin with radius r: x^2 + y^2 + z^2 = r^2. A horizontal plane z = k intersects it in x^2 + y^2 = r^2 − k^2, which is a circle of radius sqrt(r^2 − k^2) (degenerates to a point if |k| = r, or no intersection if |k| > r).
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