Perimeter and surface area of skewed end semi cylinder

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Discussion Overview

The discussion centers on calculating the surface area and perimeter of a skewed end semi-cylinder, particularly focusing on the complexities introduced by the skew angle and the shape of the end profile. The scope includes theoretical considerations and mathematical reasoning related to geometry and engineering drawing.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to calculate the surface area of a semi-cylinder with skewed ends, noting that if the skew plane is perpendicular to the cylinder axis, the end profile is a half ellipse.
  • The same participant indicates that if the skew plane is not perpendicular, the end profile becomes more complex, involving a skewed ellipse with a bevel.
  • The participant specifies parameters for the problem, including a radius of 1m, a length of 100m, and a skew angle of 45 degrees.
  • Another participant encourages the original poster to share their attempts and specific points of confusion to facilitate assistance.
  • A further contribution mentions using engineering drawing techniques to approximate the lateral area by dividing it into smaller strips, indicating a focus on the lateral surface area and boundary calculations.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants exploring different aspects of the problem without reaching a consensus on the methodology or solution.

Contextual Notes

The discussion highlights the complexity of calculating areas for skewed geometries, with assumptions regarding the nature of the skew and the shapes involved remaining unverified. There are also references to multi-radius arches, which introduce additional complexity.

smstoankur
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I want to calculate the surface area of semi cylinder with one or both ends skew at a given angle. To calculate the area/perimeter i need to find out the end profile of the semi cylinder.
If the skew plane is perpendicular to the cylinder axis, the cut surface would be half ellipse with major axis skewed at the angle and minor axis equal to the radius of the semi cylinder. In this case the surface area can be easily calculated since the end part can be easily identified.
But if the skew plane is not perpendicular to the cylinder axis, then the end part would be skew along with bevel. In this case, the end part is again ellipse. I want to calculate the surface area of the semi cylinder for the second part. Please assume the radius to be 1m and length as 100m. The skew angle is 45 degrees at the end and inclined at 45 degrees to the perpendicular axis. Please help me solve this problem.
 
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welcome to pf!

hi smstoankur! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
Hi tiny-tim,

I am only interested in the approximate lateral area of the top part of semi cylinder so I tried solving it using engineering drawing by diving it into number of smaller strips and adding the total. I have attached the two problems which I explained before. The problem I discussed is with the semi circular ends so it is easy to work with. But I have to work with multi radius arches which can be difficult to work with. I am only interested in the lateral surface area. If I can calculate the boundary then I can work out the area by approximation. I was looking for a generalized solution for calculation of the boundary in different cases.
 

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