Elliptic Paraboloid
- Elliptic paraboloid (a three-dimensional figure) has a u-shaped curve with an elliptical end.
Height of a Elliptic Paraboloid formula |
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| \(\large{ h = p \; a^2 }\) | ||
| 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 |
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| \(\large{ L = \frac{\pi \; a}{ \left(6\;h^2 \right) \; \left[ \left(a^2 \;+\; 4\;h^2 \right) ^{\frac{3}{2} } \; a^3 \right] } }\) | ||
| 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 |
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| \(\large{ S = L + \pi \; a^2 }\) | ||
| 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 |
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| \(\large{ V= \frac{1}{2} \; \pi \; a^2 \;h }\) | ||
| 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