# Elliptic Paraboloid

Written by Jerry Ratzlaff 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

$$\large{ h = p \; a^2 }$$

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

Tags: Equations for Volume