Surface area of revolution for an ellipse

Thread starter erjkism
Start date Mar 10, 2008
Tags

Area Ellipse Revolution Surface Surface area

In summary, the surface area of revolution for an ellipse is calculated using the formula A = 2πab, where a is the length of the semi-major axis and b is the length of the semi-minor axis. It differs from the surface area of a circle because it takes into account the different lengths of the semi-major and semi-minor axes. The surface area of revolution for an ellipse can never be negative and will change depending on the values of a and b, as well as the rotation axis.

Mar 10, 2008

erjkism

Homework Statement

Find the surface area obtained when the upper half of the ellipse: [tex]\frac{x^{2}}{4}+ y^{2}=1[/tex] is rotated about the x-axis

Homework Equations

[tex]\int2piyds[/tex]

The Attempt at a Solution

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Mar 10, 2008

Dick

Science Advisor

Homework Helper

Please continue. ds=sqrt(1+(dy/dx)^2)*dy, correct?

Related to Surface area of revolution for an ellipse

1. What is the formula for finding the surface area of revolution for an ellipse?

The formula for finding the surface area of revolution for an ellipse is A = 2πab, where a is the length of the semi-major axis and b is the length of the semi-minor axis.

2. How is the surface area of revolution for an ellipse different from a circle?

The surface area of revolution for an ellipse is different from a circle because it takes into account the different lengths of the semi-major and semi-minor axes, while the surface area of a circle only considers the radius.

3. Can the surface area of revolution for an ellipse be negative?

No, the surface area of revolution for an ellipse cannot be negative. It is always a positive value and represents the total area of the curved surface formed when the ellipse is rotated around its axis.

4. How does changing the values of a and b affect the surface area of revolution for an ellipse?

Changing the values of a and b will change the overall shape and size of the ellipse, and therefore, will also affect the surface area of revolution. As the values of a and b increase, the surface area of revolution will also increase.

5. Does the surface area of revolution for an ellipse change if it is rotated around different axes?

Yes, the surface area of revolution for an ellipse will change if it is rotated around different axes. This is because the rotation axis affects the shape of the resulting surface and therefore, the surface area.