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A sphere is given by x² + y² + z² + 2x - 2y - 4z - 19 = 0. If it is intersected by the plane x + 2y + 2z + 7 = 0, what is the radius of the resulting circular section?

1. 4
2. 1
3. 2
4. 3

Correct answer: 3

Solution

To find the radius of the circular section formed by the intersection of the sphere and the plane, we first rewrite the sphere's equation in standard form to identify its center and radius. The center is at (-1, 1, 2) and the radius is 5. The distance from the center to the plane is calculated, and using the Pythagorean theorem, we find the radius of the circular section to be 3.

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