Find an equation of the largest sphere with center (14, 8, 5) that is contained completely in the first octant.

Question

Find an equation of the largest sphere with center (14, 8, 5) that is contained completely in the first octant.

Answer 1

Jacob,

The equation of a sphere is just a one dimension expansion of the circle equation.

 

(x-h)² + (y-j)² + (z-k)² = r²

 

where (h, j, k) is the center of the sphere and r is the radius.

You're given the center, so the only remaining task is finding the radius.

Because the z dimension is the smallest at 5, the radius is limited to 5, beyond which it crosses the xy plane.

So the equation is:

 

(x-14)² + (y-8)² + (z-5)² = 25