perimeter and overall surface area of skewed end semi cylinder

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.

Re: perimeter and overall surface area of skewed end semi cylinder

Hey smstoankur.

Have you done any vector calculus? There are results that relate surface integrals (finding areas of a surface) to an actual object in three-dimensional space.

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Re: perimeter and overall surface area of skewed end semi cylinder

Hi Chiro,

I haven't done vector calculus. I was working by dividing the surface area into strips and then adding up. This is a part of CAD problem so I just need the approximate lateral area.

I have attached the two problems which I explained before. I did it using engineering drawing. In this case the ends is semi circle 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.

Re: perimeter and overall surface area of skewed end semi cylinder

Done. How to delete this post?