Right Elliptic Cylinder

on . Posted in Solid Geometry

  • elliptic cylinder 2Elliptic cylinder (a three-dimensional figure) has a cylinder shape with elliptical ends.
  • 2 bases

 

 

 

 

 

 

 

 

Since there is no easy way to calculate the ellipse perimeter with high accuracy.  Calculating the laterial surface will be approximate also.

elliptic cylinder 6

Lateral Surface Area of a Right Elliptic Cylinder formula

\(\large{ A_l \approx  h \;  \left(     2\;\pi \;\sqrt {\; \frac{1}{2}\; \left(a^2 + b^2 \right) }   \right)   }\) 
Symbol English Metric
\(\large{ A_l }\) = approximate lateral surface area (side) \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ a }\) = length semi-major axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ b }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)

 

elliptic cylinder 6

Surface Area of a Right Elliptic Cylinder formula

\(\large{ A_s \approx  h \;  \left(     2\;\pi \;\sqrt {\; \frac{1}{2}\; \left(a^2 + b^2 \right) }   \right) +  2\; \left( \pi \; a \; b \right)  }\) 
Symbol English Metric
\(\large{ A_s }\) = approximate surface area (bottom, top, side) \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ a }\) = length semi-major axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ b }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)

 

elliptic cylinder 6

Volume of a Right Elliptic Cylinder formula

\(\large{ V = \pi\; a \;b\; h }\) 
Symbol English Metric
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ a }\) = length semi-major axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ b }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)

 

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Tags: Volume Equations