# Sphere equation

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• Sep 23rd 2010, 07:30 PM
Truthbetold
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!
• Sep 23rd 2010, 09:07 PM
Soroban
Hello, Truthbetold!

Quote:

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

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.

$\displaystyle \text{The distance between the planes }\,x = 2\,\text{ and }\,x = 6\,\text{ is }\,4\text{ units.}$
. . 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.

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

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

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

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

Go for it!