Confused by Spherical Wedge Graphing on z-y Plane

In summary, part (a) of the conversation discusses setting up a triple integral and part (b) raises a question about the placement of the spherical wedge in the diagram provided by the solutions manual. The speaker explains that the lines on the diagram represent cones with a fixed angle with the z-axis and the intersection with the z-y plane was drawn for illustrative purposes.
  • #1
Dethrone
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View attachment 4461

Part (a) is easy to do by setting up a triple integral, but for part (b), I was a bit confused by the diagram provided by the solutions manual:
View attachment 4462

Why is the spherical wedge (shaded) graphed on the z-y axis? In the most general case, shouldn't the two lines that form angle $\phi_1$ and $\phi_2$ be arbitrarily placed (such that $\phi < \pi /2$) and not necessarily lying on the z-y plane? Since it is to my understanding that $\phi$ is measured from the positive z-axis in any direction away from it, or did they draw it on the z-y plane for illustrative purposes?
 

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  • #2
Hey Rido! (Smile)

You're quite right. Those lines represent cones that have a fixed angle with the z axis.
Indeed, it's for illustrative purposes that only the intersection with the z-y-plane has been drawn. (Wasntme)
 

FAQ: Confused by Spherical Wedge Graphing on z-y Plane

What is a spherical wedge graph?

A spherical wedge graph is a type of graph that is used to represent a three-dimensional object on a two-dimensional plane. It is typically used to show the relationship between two variables, with one variable represented on the x-axis and the other variable represented on the y-axis.

How is a spherical wedge graph different from a regular graph?

A spherical wedge graph is different from a regular graph in that it represents a three-dimensional object, while a regular graph only represents two variables. This allows for a more comprehensive visualization of the relationship between the two variables.

What is the z-y plane in a spherical wedge graph?

The z-y plane in a spherical wedge graph refers to the plane on which the graph is drawn. It is defined by the z-axis, which represents the height or depth of the three-dimensional object, and the y-axis, which represents the width or length of the object.

How do I interpret a spherical wedge graph?

To interpret a spherical wedge graph, you should first look at the shape of the graph. The shape will give you an idea of the overall relationship between the two variables. You should also pay attention to the orientation of the graph, as this can indicate the direction of the relationship between the variables.

What does the shading in a spherical wedge graph represent?

The shading in a spherical wedge graph represents the different values of the third variable, which is typically represented by color. This allows for a more detailed visualization of the relationship between the two variables and the third variable.

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