Elliptic Paraboloid

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

 

Height of a Elliptic Paraboloid formula

\(\large{ h = p \; a^2  }\)

Where:

\(\large{ h }\) = height

\(\large{ a }\) = length semi-minor axis

\(\large{ p }\) = shape parameter

 

Lateral Area of a Elliptic Paraboloid formula

\(\large{ L =  \frac{\pi \; a}{  \left(6\;h^2  \right) \; \left[  \left(a^2 \;+\; 4\;h^2 \right) ^{\frac{3}{2} } \; a^3  \right]    }  }\)

Where:

\(\large{ L }\) = lateral surface

\(\large{ h }\) = height

\(\large{ a }\) = length semi-minor axis

\(\large{ \pi }\) = Pi

 

Surface Area with Base of a Elliptic Paraboloid formula

\(\large{ S =  L + \pi \; a^2  }\)

Where:

\(\large{ S }\) = surface area

\(\large{ L }\) = lateral surface

\(\large{ a }\) = length semi-minor axis

\(\large{ \pi }\) = Pi

 

Volume of a Elliptic Paraboloid formula

\(\large{ V= \frac{1}{2} \; \pi \; a^2 \;h   }\)

Where:

\(\large{ V }\) = volume

\(\large{ h }\) = height

\(\large{ a }\) = length semi-minor axis

\(\large{ \pi }\) = Pi