Surface area inside an elliptic cylinder

In summary, the task is to find the surface area of the portion of the plane 8x+3y+z=9 that is contained within the elliptic cylinder (x^2/64) + (y^2/9) =1. The necessary equations may involve parametrization of a region. In the discussion, it is suggested to view the problem as a projection and to divide the base area of the cylinder by the appropriate cosine. Further clarification is needed on how to express this as a projection and what the appropriate cosine refers to.
  • #1
MasterWu77
21
0

Homework Statement



Find the surface area of that part of the plane 8x+3y+z=9 that lies inside the elliptic cylinder (x^2/64) + (y^2/9) =1

Homework Equations



not sure what equations i need to use. probably parametrization of a region

The Attempt at a Solution



i'm not quite sure how to start this problem. how do i related the elliptic cylinder with the plane?
 
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  • #2
Hi MasterWu77! :smile:

You could just say it's a projection, and divide the base area of the cylinder by the appropriate cosine. :wink:
 
  • #3
ok but how would i say that it is a projection and what exactly do you mean by the appropriate cosine?
 

1. What is the formula for finding the surface area inside an elliptic cylinder?

The formula for finding the surface area inside an elliptic cylinder is A = 2πab + 2πb2, where a and b are the semi-major and semi-minor axes of the ellipse base of the cylinder.

2. How do you find the semi-major and semi-minor axes of an ellipse?

The semi-major and semi-minor axes of an ellipse can be found by measuring the distance from the center of the ellipse to the farthest point on the edge in each direction. These measurements are also known as the major and minor radii.

3. Can the surface area inside an elliptic cylinder be greater than the surface area of its curved surface?

Yes, the surface area inside an elliptic cylinder can be greater than the surface area of its curved surface. This is because the curved surface area only takes into account the outer surface of the cylinder, while the surface area inside also includes the area of the two flat bases.

4. How does the surface area inside an elliptic cylinder compare to that of a circular cylinder?

The surface area inside an elliptic cylinder is typically greater than that of a circular cylinder with the same height and base radius. This is because the elliptic shape allows for more surface area on the curved surface, and the flat bases add additional surface area as well.

5. Can the surface area inside an elliptic cylinder be calculated if the exact dimensions are unknown?

No, the surface area inside an elliptic cylinder cannot be calculated if the exact dimensions are unknown. The semi-major and semi-minor axes of the ellipse, as well as the height and base radius, are all necessary to accurately calculate the surface area inside the cylinder.

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