Elliptic Paraboloid

on . Posted in Solid Geometry

  • Elliptic paraboloid (a three-dimensional figure) has a u-shaped curve with an elliptical end.

 

elliptic paraboloid 3

Height of a Elliptic Paraboloid formula

\(\large{ h = p \; a^2  }\) 
Symbol English Metric
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ a }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ p }\) = shape parameter \(\large{ in }\) \(\large{ mm }\)

 

 

elliptic paraboloid 3

Lateral Area of a Elliptic Paraboloid formula

\(\large{ L =  \frac{\pi \; a}{  \left(6\;h^2  \right) \; \left[  \left(a^2 \;+\; 4\;h^2 \right) ^{\frac{3}{2} } \; a^3  \right]    }  }\) 
Symbol English Metric
\(\large{ L }\) = lateral surface area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ a }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)

 

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Surface Area with Base of a Elliptic Paraboloid formula

\(\large{ S =  L + \pi \; a^2  }\) 
Symbol English Metric
\(\large{ S }\) = surface area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ L }\) = lateral surface area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ a }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)

 

elliptic paraboloid 3

Volume of a Elliptic Paraboloid formula

\(\large{ V= \frac{1}{2} \; \pi \; a^2 \;h   }\) 
Symbol English Metric
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ a }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)

 

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Tags: Volume Equations