# Math Help - Sphere in the First Octant

1. ## Sphere in the First Octant

Hi im having trouble with this problem.
Find an equation of the largest sphere with the given center that is contained in the first octant. (6, 4, 9)

So I thought that the radius would be distance from the center to the origin.
I get 36+16+81=133 for my r squared

so i submitted this equation and don't have it right. i feel like its something simple im missing
$(x-6)^2+(y-4)^2+(z-9)^2=133$

2. Originally Posted by fizzle45
Hi im having trouble with this problem.
Find an equation of the largest sphere with the given center that is contained in the first octant. (6, 4, 9)

So I thought that the radius would be distance from the center to the origin.
I get 36+16+81=133 for my r squared

so i submitted this equation and don't have it right. i feel like its something simple im missing
$(x-6)^2+(y-4)^2+(z-9)^2=133$
The radius would have to be 4. Given the coordinates of the center, we know it can't be 9 units (otherwise it passes the xz and yz planes (going outside of the first octant), and it can't 6 units, since it will pass the xz plane.

Thus, the only suitable radial value would be 4.

Therefore, the equation of the sphere is $(x-6)^2+(y-4)^2+(z-9)^2=16$