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# Paraboloid Surface Area and Volume Calculator

A paraboloid is a solid of revolution that results from rotating a parabola around its axis of symmetry. If you know the height and radius of a paraboloid, you can compute its volume and surface area with simple geometry formulas. You can also use the calculator on the left.

### Volume Formula

If the height of a paraboloid is denoted by*h*and the radius by

*r*, then the volume is given by the equation

V = (π/2)hr²

Notice that this is less than the volume of a cylinder but more than the volume of a cone with the same dimensions.

### Surface Area Formula

The surface area of a paraboloid, not including its base, is given by the formulaSA = (π/6)(r/h²)[(r² + 4h²)

^{3/2}- r³]

Since the base of the figure has an area of πr², the formula for surface area including the base is

SA

_{b}= (π/6)(r/h²)[(r² + 4h²)

^{3/2}- r³] + πr²

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