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Elliptic Paraboloid

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Volume

Height of a Elliptic Paraboloid formula
$h \;=\; p \cdot a^2$
Symbol	English	Metric
$h$ = height	$in$	$mm$
$a$ = length semi-minor axis	$in$	$mm$
$p$ = shape parameter	$in$	$mm$

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

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

Surface Area with Base of a Elliptic Paraboloid formula
$S \;=\; L + \pi \cdot a^2$
Symbol	English	Metric
$S$ = surface area	$in^2$	$mm^2$
$L$ = lateral surface area	$in^2$	$mm^2$
$a$ = length semi-minor axis	$in$	$mm$
$\pi$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$

Volume of a Elliptic Paraboloid formula
$V \;=\; \dfrac{1}{2} \cdot \pi \cdot a^2 \cdot h$
Symbol	English	Metric
$V$ = volume	$in^3$	$mm^3$
$h$ = height	$in$	$mm$
$a$ = length semi-minor axis	$in$	$mm$
$\pi$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$

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