# 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

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

### Lateral Area of a Elliptic Paraboloid formula

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

### Surface Area with Base of a Elliptic Paraboloid formula

$$S = L + \pi \; a^2$$
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 $$3.141 592 653 ...$$

### Volume of a Elliptic Paraboloid formula

$$V = \frac{1}{2} \; \pi \; a^2 \;h$$
Symbol English Metric
$$V$$ = volume $$in^3$$ $$mm^3$$
$$h$$ = height $$in$$ $$mm$$
$$a$$ = length semi-minor axis $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$

Tags: Volume