1. ## Sphere equation

Find an equation of the largest sphere contained in the cube determined by the planes x = 2, x = 6,; y = 5, y = 9; and z = -1, z = 3.

I'm going to guess that I need to use the distance formula. I don't know how to apply the result to this problem, however.

Are these plains the boundaries of the sphere with the distance being the diameter?

Thanks!

2. Hello, Truthbetold!

Find an equation of the largest sphere contained in the cube
determined by the planes: . $x = 2,\;x = 6,\;y = 5,\;y = 9,\;z = -1,\;z = 3$

Are these planes the boundaries of the sphere with the distance being the diameter?
Yes!

You don't need the Distance Formula . . . just some visualization.

$\text{The distance between the planes }\,x = 2\,\text{ and }\,x = 6\,\text{ is }\,4\text{ units.}$
. . And they said it was a cube, didn't they?

Can you see that the radius of the sphere is 2 ?

The center of the sphere must be halfway between the planes.

$\text{Halfway between the planes }\,x = 2\,\text{ and }\,x = 6\!:\; x = 4$

$\text{Halfway between the planes }\,y = 5\,\text{ and }\,y = 9\!:\; y = 7$

$\text{Halfway between the planes }\,z = \text{-}1\,\text{ and }\,z = 3\!:\; z = 1$

The center is $(4,7,1)$ and the radius is 2.

Go for it!