How Can I Visualize the Intersection of a Cone and a Sphere?

In summary, the conversation discusses finding the volume of a solid enclosed by a cone and a sphere, and the use of cylindrical and spherical coordinates to set up the integral. The speaker is seeking a visualization tool to graph both regions simultaneously. A possible source for information on "spherical cone" is mentioned.
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Dethrone
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Find the volume of the solid that is enclosed by the cone $z=\sqrt{x^2+y^2}$ and the sphere $x^2+y^2+z^2=2$.

The integral is not difficult to set up using cylindrical coordinates, but I'm trying to get a better visualization of the volume I'm actually integrating. I can't seem to get Wolfram Alpha to graph both regions at the same time. Is there any way I can do that, or even better, have it to shade in that region?

(I have been able to graph it by hand, but it is a terrible sketch :( )
 
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FAQ: How Can I Visualize the Intersection of a Cone and a Sphere?

What is graphing multivariable regions?

Graphing multivariable regions is a mathematical concept that involves plotting and visualizing regions in a coordinate system with more than two variables. It is often used in fields such as economics, physics, and engineering to study complex relationships between multiple variables.

Why is it important to graph multivariable regions?

Graphing multivariable regions allows us to better understand the relationships between multiple variables and how they affect each other. It also helps us to identify patterns and trends that may not be apparent when looking at individual variables.

What types of functions can be used to graph multivariable regions?

Commonly used functions for graphing multivariable regions include linear, quadratic, exponential, and logarithmic functions. However, any function that involves more than two variables can be used for this purpose.

What are some techniques for graphing multivariable regions?

One technique is to use level curves, which are curves that represent points on a surface where the function has a constant value. Another technique is to use 3D graphs, which can show the relationship between three variables. Additionally, using technology such as graphing calculators or computer programs can also be helpful in visualizing multivariable regions.

How can graphing multivariable regions be applied in real-world situations?

Graphing multivariable regions is commonly used in fields such as economics, physics, and engineering to analyze and predict complex relationships between multiple variables. It can also be applied in data analysis to identify patterns and trends in large datasets with multiple variables. Additionally, it can aid in decision making and problem-solving by providing a visual representation of complex systems and relationships.

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