Surface area and parametric equations

Thread starter th3plan
Start date Apr 28, 2008
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Area Parametric Parametric equations Surface Surface area

In summary, surface area is the total area of the outer surface of a three-dimensional object and is calculated by adding the areas of all its faces. Parametric equations are used to represent surfaces by using two or three equations with parameters. This allows for more flexibility in representing complex shapes. Regular surfaces are described using a single equation, while parametric surfaces use multiple equations. Surface area and parametric equations are related as the latter can be used to calculate the former. However, parametric equations are not able to represent all types of surfaces and are most commonly used for curved surfaces.

Apr 28, 2008

th3plan

I just have a question, when I am rotating something let's say around y=2 and the two equations are x=t^3 + 1 and y = 4t+1

how would i set it up?

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Apr 28, 2008

Dick

Science Advisor

Homework Helper

That's not a very good attempt. TRY to set it up, and if it's wrong somebody will try to help. If you don't TRY, I doubt anyone will help.

Related to Surface area and parametric equations

1. What is surface area and how is it calculated?

Surface area refers to the total area of the outer surface of a three-dimensional object. It is calculated by finding the sum of the areas of all the faces of the object. For example, the surface area of a cube is calculated by multiplying the length of one side by itself and then multiplying that by 6 (since there are 6 faces on a cube).

2. How are parametric equations used to represent surfaces?

Parametric equations are used to represent surfaces by using two or three equations that express the coordinates of points on the surface in terms of one or more parameters. These equations are often used in situations where traditional equations are not able to accurately describe the shape or behavior of a surface.

3. What is the difference between a parametric surface and a regular surface?

A regular surface is described using a single equation, such as a function of x and y. A parametric surface, on the other hand, uses multiple equations with one or more parameters to describe the surface. This allows for more flexibility in representing complex or irregular shapes.

4. How are surface area and parametric equations related?

Surface area and parametric equations are related because parametric equations can be used to determine the surface area of a parametric surface. By finding the derivatives of the parametric equations and using those values to calculate the surface area, the total area of the surface can be determined.

5. Can parametric equations be used to represent any type of surface?

No, parametric equations are not able to represent every type of surface. They are most commonly used to represent curved surfaces, such as spheres, ellipsoids, and tori. They are also limited in their ability to represent surfaces with sharp corners or edges.