What is the radius of the sphere passing through origin and concentric with the sphere S ?
For the next two (02) items that follow : The equation of the sphere S is \( x^2 + y^2 + z^2 - 4x - 6y - 12z + k = 0 \).
- A. \frac{7}{2}
- B. 5
- C. 7 ✓
- D. Cannot be determined due to insufficient data
Correct Answer: C. 7
Explanation
The center of S is (2, 3, 6). The radius of the concentric sphere passing through the origin (0, 0, 0) is the distance from the origin to the center: \sqrt{2^2 + 3^2 + 6^2} = \sqrt{49} = 7.
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