Find an equation or inequality that describes the following object. A ball with center \( (-6,4,1) \) and radius 6 . Choose the correct answer below. A. \( (x-6)^{2}+(y+4)^{2}+(z+1)^{2} \geq 36 \) B. \( (x+6)^{2}+(y-4)^{2}+(z-1)^{2}=36 \) C. \( (x+6)^{2}+(y-4)^{2}+(z-1)^{2} \leq 36 \) D. \( (x-6)^{2}+(y+4)^{2}+(z+1)^{2} \leq 36 \)

To describe a ball with center \((-6, 4, 1)\) and radius 6, we use the equation of a sphere. The general formula is \((x - h)^{2} + (y - k)^{2} + (z - l)^{2} = r^{2}\), where \((h, k, l)\) is the center and \(r\) is the radius. Given the center \((-6, 4, 1)\) and radius \(6\), the equation becomes: \[ (x + 6)^{2} + (y - 4)^{2} + (z - 1)^{2} = 36 \] Hence, the correct answer is **B**. As a side note, if the question were about the solid ball instead of just the surface, we'd use the inequality: \[ (x + 6)^{2} + (y - 4)^{2} + (z - 1)^{2} \leq 36. \]