Surface area bounded by 2 different planes

In summary, the discussion is about finding the surface area of a portion of a plane that lies above a disc in the first octant. The disc is described as having a radius of √2 and lying on the xy plane with z = 0. The author provided a solution but the other person thinks it's wrong and should include the green area as well. However, the author clarifies that it is only the black area that needs to be considered.
  • #1
chetzread
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Homework Statement


Find the surface area of portion of plane x + y + z = 3 that lies above the disc (x^2) + (y^2) < 2 in the first octant ...

Homework Equations

The Attempt at a Solution


Here's the solution provided by the author ...
I think it's wrong ... I think it should be the green coloured area + the black area ...

If it's only the black area , then the problem is find the surface area of portion of plane x + y + z = 3 that lies above the cylinder (x^2) + (y^2) < 2 in the first octant..
 
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  • #3
chetzread said:

Homework Statement


Find the surface area of portion of plane x + y + z = 3 that lies above the disc (x^2) + (y^2) < 2 in the first octant ...

Homework Equations

The Attempt at a Solution


Here's the solution provided by the author ...
I think it's wrong ... I think it should be the green coloured area + the black area ...
No, it's just the black area.
chetzread said:
If it's only the black area , then the problem is find the surface area of portion of plane x + y + z = 3 that lies above the cylinder (x^2) + (y^2) < 2 in the first octant..
That's not what they wrote. The disc they described consists of all the points in the x-y plane that lie inside the circle ##x^2 + y^2 = 2##.
 
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  • #4
Mark44 said:
No, it's just the black area.
That's not what they wrote. The disc they described consists of all the points in the x-y plane that lie inside the circle ##x^2 + y^2 = 2##.
The disc here refers to the circle with radius 2 lie on the xy plane where z = 0?
 
  • #5
chetzread said:
The disc here refers to the circle with radius 2 lie on the xy plane where z = 0?
Almost -- the radius is ##\sqrt{2}##. And yes, the disc is in the x-y plane.
 

Related to Surface area bounded by 2 different planes

1. What is the formula for finding the surface area bounded by 2 different planes?

The formula for finding the surface area bounded by 2 different planes is given by S = 2ab + 2bc + 2ac, where a, b, and c represent the lengths of the sides of the rectangular prism formed by the two planes.

2. How does the angle between the two planes affect the surface area?

The angle between the two planes does not affect the surface area. As long as the lengths of the sides of the rectangular prism formed by the planes remain the same, the surface area will remain constant.

3. Can the surface area bounded by 2 different planes be negative?

No, the surface area bounded by 2 different planes cannot be negative. Surface area is a measure of the total area of a 3-dimensional object, and therefore, cannot have a negative value.

4. What factors can affect the surface area bounded by 2 different planes?

The surface area bounded by 2 different planes can be affected by the lengths of the sides of the rectangular prism formed by the planes, as well as the shape and orientation of the planes relative to each other.

5. Can the surface area bounded by 2 different planes be calculated for non-rectangular shapes?

Yes, the surface area bounded by 2 different planes can be calculated for non-rectangular shapes using the appropriate formulas for finding the surface area of that particular shape. However, it may be more complex to calculate compared to a rectangular prism.

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