Calc III, Inequalitites problem!

  • Thread starter mr_coffee
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  • #1
mr_coffee
1,629
1
Hello everyone, I'm having some troubles figuring this out. I'm supppose to Describe the set of points whose coordinates satisfy the given equations and inequalitites. Sketch the graph.

x^2 + y^2 + z^2 ≤ 16, 2 ≤ y ≤ 4;

I forgot the rules of inequalitites, I see its an equation of a sphere and the plane is going to be parallel to the xz-plane but I'm lost after that. Any help would be great! thanks!
 

Answers and Replies

  • #2
balakrishnan_v
50
0
What is the question?
If you are supposed to find the volume:
The answer is 40pi/3
If you are supposed to find the curved surface area,it is:16pi
If you are supposed to find the total surface area,it is 28pi
 
  • #3
whozum
2,221
1
balakasldkfaje, your answers are all irrelevant. Coffee, it wants you to describe the surface of intersection. The first equation is a ball (almost literally), and the second is a block. If you have some graphing software its easy to see but I can understand why your having difficulty imagining these.

They intersect and make a funny lookin shape, kinda like if you hsaved the head off of a tennis ball.
 
  • #4
Fermat
Homework Helper
872
1
The 1st inequality is a solid sphere. The 2nd inequality limits the values of y-coordintes.

In fact, it's only the top quarter of the tennis ball that is left.From y = 2 to y = 4.
 

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