Elliptic Paraboloid

on . Posted in Solid Geometry

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

Height of a Elliptic Paraboloid formula

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

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  $$\large{3.141 592 653 ...}$$

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  $$\large{3.141 592 653 ...}$$

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  $$\large{3.141 592 653 ...}$$

Tags: Volume Equations