[SOLVED] Sphere equation

Hello, Truthbetold!

Quote:

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!