Which is the equation for a sphere with the center (8,-6,6) and radius 6?

(x - 8) ² + (y+6) ² + (z-6) ² = 36

Step-by-step explanation:

To find the equation for a sphere with the center (8,-6,6) and radius 6, we will follow the steps below;

first write down the standard equation of a sphere:

(x - h) ² + (y-k) ² + (z-l) ² = R²

where h, k and l are the center and R is the radius

From the question given, h = 8, k = -6 l=6 and R=6

we can now substitute the values into the formula

(x - h) ² + (y-k) ² + (z-l) ² = R²

(x - 8) ² + (y+6) ² + (z-6) ² = 6²

(x - 8) ² + (y+6) ² + (z-6) ² = 36

Therefore, the equation for a sphere with the center (8,-6,6) and radius 6 is

(x - 8) ² + (y+6) ² + (z-6) ² = 36