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 need to use the standard formula for the equation of a sphere, which is given by \( (x - h)^{2} + (y - k)^{2} + (z - l)^{2} = r^{2} \), where \( (h, k, l) \) is the center and \( r \) is the radius. From the given center \( (-6, 4, 1) \), we substitute into the formula: \[ (x + 6)^{2} + (y - 4)^{2} + (z - 1)^{2} = 6^2 \] This simplifies to: \[ (x + 6)^{2} + (y - 4)^{2} + (z - 1)^{2} = 36 \] Thus, the correct answer is: **B. \( (x+6)^{2}+(y-4)^{2}+(z-1)^{2}=36 \)** For a bit of fun: did you know that the concept of a ball in mathematics is often used in higher dimensions? While we often think of spheres in 3D, mathematicians study "balls" in 4D (and even beyond) — and they get even wilder! If you're fascinated by geometry, dive into the world of topology! It’s a branch of mathematics that expands on these concepts, exploring properties even more bizarre than the shapes and spaces we know. Grab a good book on topology and prepare to have your mind blown!