Calc III, Inequalitites problem

  • Thread starter Thread starter mr_coffee
  • Start date Start date
  • Tags Tags
    Calc iii
AI Thread Summary
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
Messages
1,613
Reaction score
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!
 
Physics news on Phys.org
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.
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Describe the set of points Calc III equation of sphere
Replies
10
Views
6K
Depth of a basketball floating on water
Replies
9
Views
897
Calc III, what point could this be?
Replies
8
Views
2K
A couple of calc III, 3d drawings & sphere problems
Replies
4
Views
4K
Why doesn't my solution for finding a plane through three points work?
Replies
3
Views
2K
Infinite Wire/Surface charge question
Replies
2
Views
1K
Finding the moment(s) of inertia
Replies
2
Views
3K
Solving Calc III Plane Equation with y=1, z=2
Replies
4
Views
8K
Finding the Centre of Mass of a Hemisphere
Replies
13
Views
3K
Gravitational forces, speeds and masses
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top