Cal3 cyliderical spherical coords

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In summary, "Cal3 cylindrical spherical coordinates" are a type of coordinate system used in mathematics and physics to describe the position of a point in three-dimensional space. They combine elements of both the cylindrical and spherical coordinate systems, resulting in a more accurate way to describe location. These coordinates are commonly used in various fields of science, including physics, astronomy, and engineering, due to their ability to accurately describe the position of objects and make calculations involving distance, direction, and angles easier. However, they may not always be the most convenient or efficient option, particularly in cases where the point is located close to the origin or along the x, y, or z axis.
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Eunix1992
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Homework Statement



find the volume between the cone x=√y^2+z^2, and the spherex^2+y^2+z^2=196

Homework Equations





The Attempt at a Solution


for x=√y^2+z^2, I got x^2=y^2+z^2, and 2x^2=196, x=98, for this, I don't know what i am supposed to do then. Thanks!
 
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sorry,. x^2=98. but what can i do then? thanks.
 

What are "Cal3 cylindrical spherical coordinates"?

"Cal3 cylindrical spherical coordinates" are a type of coordinate system used in mathematics and physics to describe the position of a point in three-dimensional space. It combines the cylindrical coordinate system (which uses the distance from a fixed point, an angle, and a height) with the spherical coordinate system (which uses the distance from a fixed point, two angles, and a direction). This results in a more accurate and comprehensive way to describe the location of a point in space.

What is the difference between cylindrical and spherical coordinates?

The main difference between cylindrical and spherical coordinates is the number of variables used to describe the position of a point. Cylindrical coordinates use three variables (radius, angle, and height) while spherical coordinates use four variables (radius, two angles, and direction). Additionally, the two systems use different shapes as a reference point - cylindrical coordinates use a cylinder, while spherical coordinates use a sphere.

How are Cal3 cylindrical spherical coordinates used in science?

Cal3 cylindrical spherical coordinates are used in various fields of science, including physics, astronomy, and engineering. They are particularly useful for describing the position of objects in three-dimensional space, such as the location of stars and planets in the night sky or the coordinates of a point in a 3D graph. They can also be used in calculations involving distance, direction, and angles.

What are the advantages of using Cal3 cylindrical spherical coordinates?

One of the main advantages of using Cal3 cylindrical spherical coordinates is the ability to accurately describe the position of a point in three-dimensional space. This is particularly useful in situations where using other coordinate systems, such as Cartesian coordinates, may be more complex or less accurate. Additionally, Cal3 cylindrical spherical coordinates can make certain calculations, such as finding the distance between two points, easier and more intuitive.

Are there any limitations to using Cal3 cylindrical spherical coordinates?

While Cal3 cylindrical spherical coordinates are useful in many situations, they do have some limitations. One limitation is that they are not always the most convenient or efficient way to describe a point in space. For example, in situations where the point is located close to the origin or along the x, y, or z axis, cylindrical or spherical coordinates may not be the most practical option. In these cases, other coordinate systems may be more appropriate.

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