Calc III, Inequalitites problem

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The discussion centers on understanding the geometric representation of the inequalities x^2 + y^2 + z^2 ≤ 16 and 2 ≤ y ≤ 4. The first inequality describes a solid sphere with a radius of 4, while the second restricts the y-coordinates to a range between 2 and 4, effectively slicing the sphere. This results in a shape resembling the top quarter of a sphere, akin to the upper part of a tennis ball. Participants clarify that the task involves describing the surface of intersection rather than calculating volume or surface area. The graphical representation can aid in visualizing this intersection more clearly.
mr_coffee
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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!
 
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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
 
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.
 
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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