# Sketch the surface of a paraboloid

• CricK0es
In summary: Sketch the cross-sectional shape in each plane and then use the equation of the circle to find the radius of the circle.In summary, the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space has a cross-sectional shape that is found by sketching cross sections in a number of planes that are parallel to the x-y plane. The equation of the circle can be used to find the radius of the circle.
CricK0es

## Homework Statement

Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space

## Homework Equations

I assume partial derivatives are involved in some manner

## The Attempt at a Solution

[/B]
I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks

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CricK0es said:

## Homework Statement

Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space

## Homework Equations

I assume partial derivatives are involved in some manner

## The Attempt at a Solution

I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks [/B]
Please correct your statement of the problem. It must be in error.

What did you get when you set an individual variable to zero ?

CricK0es said:

## Homework Statement

Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space

## Homework Equations

I assume partial derivatives are involved in some manner

## The Attempt at a Solution

I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks [/B]
Y-comp is missing, So it can't be 3d shape.

CricK0es said:

## Homework Statement

Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space
Do you mean ##z = 9 - x^2 - y^2##?
CricK0es said:

## Homework Equations

I assume partial derivatives are involved in some manner
Neither ordinary derivatives nor partial derivatives are required in this problem.
CricK0es said:

## The Attempt at a Solution

[/B]
I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks
Setting one variable to zero gives you what's called a trace, the intersection of the surface in one of the coordinate planes. For example, assuming the surface is as I wrote it above, setting x = 0, gives you the trace in the y-z plane. Setting y = 0, gives you the trace in the x-z plane.

There are other techniques that can be used. Your textbook should have some examples, especially for paraboloids. These kinds of surfaces have circular cross-sections along some axis.

CricK0es
Yeah there was a mistake on the question paper, I had to email my tutor, 92 goes to y2.

CricK0es said:
Yeah there was a mistake on the question paper 92 goes to y2.

Look for cross sections in a number of planes that are parallel to the x-y plane.

CricK0es

## 1. What is a paraboloid?

A paraboloid is a three-dimensional shape that resembles a bowl or a dish. It is formed by rotating a parabola around its axis.

## 2. How do you sketch the surface of a paraboloid?

To sketch the surface of a paraboloid, you can start by drawing a parabola on a piece of paper. Then, rotate the parabola around its axis to create a bowl-shaped figure. Make sure to draw the curves accurately and symmetrically to create a smooth surface.

## 3. What are the properties of a paraboloid?

A paraboloid has a single axis of symmetry, and its cross-sections are all parabolas. It also has a vertex, which is the point where the parabola intersects with the axis of symmetry.

## 4. What are the real-life applications of a paraboloid?

Paraboloids have many practical uses in daily life. They are commonly found in satellite dishes, flashlights, and reflectors. They are also used in architecture, such as in the design of domes and archways.

## 5. Are there different types of paraboloids?

Yes, there are different types of paraboloids, including elliptic paraboloids, hyperbolic paraboloids, and circular paraboloids. Each type has a different shape and properties, but they all share the common characteristic of being formed by rotating a parabola.

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