Perimeter and surface area of skewed end semi cylinder

Click For Summary
SUMMARY

The discussion focuses on calculating the surface area of a skewed end semi-cylinder, specifically when the skew angle is 45 degrees and the cylinder has a radius of 1 meter and a length of 100 meters. When the skew plane is perpendicular to the cylinder axis, the end profile is a half-ellipse, making calculations straightforward. However, when the skew plane is not perpendicular, the end profile becomes a skewed ellipse, complicating the surface area calculation. The user seeks a generalized solution for determining the boundary of the semi-cylinder in various cases.

PREREQUISITES
  • Understanding of geometric shapes, specifically ellipses and semi-cylinders.
  • Familiarity with engineering drawing techniques for surface area approximation.
  • Knowledge of skew angles and their impact on geometric calculations.
  • Basic proficiency in calculus for area calculations involving curves.
NEXT STEPS
  • Research methods for calculating the surface area of skewed geometric shapes.
  • Learn about the properties of ellipses and their applications in engineering.
  • Explore numerical methods for approximating areas under curves.
  • Investigate software tools for 3D modeling and surface area calculations, such as AutoCAD or SolidWorks.
USEFUL FOR

Engineers, architects, and students in fields related to geometry and structural design, particularly those working with complex shapes and surface area calculations.

smstoankur
Messages
3
Reaction score
0
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.
 
Physics news on Phys.org
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.
 

Attachments

Last edited:
How to delete this thread?
 

Similar threads

Help, can't visualize a fantasy worldbuilding mechanic
  • · Replies 1 ·
Replies
1
Views
3K
Understanding why we compute surface area as we do
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
3K
Speed of cylinder rolling along a horizontal surface gathering snow (Solved)
  • · Replies 13 ·
Replies
13
Views
2K
Calculating 3D Cylinder Volumes & Areas With Constants
  • · Replies 14 ·
Replies
14
Views
3K
Tension in a deformed cylindrical bag on a surface
  • · Replies 18 ·
Replies
18
Views
2K
Undergrad Equation to graph a 180 degree curve comprised of a radius and an ellipse
  • · Replies 8 ·
Replies
8
Views
4K
Number of Decks on a Rotating Habitat
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Working out a point / segment on a sphere
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Where is the Angle Theta Measured in a Cylinder's Surface Area?
  • · Replies 1 ·
Replies
1
Views
5K