My Math Forum 3-D Surface plot of equation

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October 7th, 2017, 05:06 PM   #1
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3-D Surface plot of equation

What does the plot of this surface equation look like ?

I know it has a shape of the sphere but I am confused what is 1 and 4 and what they represent.
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 Sphere plot.JPG (13.7 KB, 7 views)

 October 7th, 2017, 06:44 PM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 535 Thanks: 306 Math Focus: Dynamical systems, analytic function theory, numerics $x^2 + y^2 + z^2 \leq 4$ describes a solid ball of radius 4. $x^2 + y^2 + z^2 \leq 1$ is similar ball of radius 1. Can you see from this what your region looks like?
October 7th, 2017, 10:16 PM   #3
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Quote:
 Originally Posted by SDK $x^2 + y^2 + z^2 \leq 4$ describes a solid ball of radius 4. $x^2 + y^2 + z^2 \leq 1$ is similar ball of radius 1. Can you see from this what your region looks like?
Is it like a ball but a hole inside of it ?

 October 7th, 2017, 10:39 PM #4 Senior Member     Joined: Sep 2015 From: USA Posts: 2,264 Thanks: 1198 half of one yes
 October 13th, 2017, 08:04 AM #5 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 "Half of one" because of the additional condition $\displaystyle z\ge 0$.

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