Volume of Paraboloid given Height Calculator

✖Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.ⓘ Height of Paraboloid [h]			+10% -10%
✖Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid.ⓘ Shape Parameter of Paraboloid [p]			+10% -10%

✖Volume of Paraboloid is the amount of three dimensional space occupied by the Paraboloid.ⓘ Volume of Paraboloid given Height [V]

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Formula

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Volume of Paraboloid given Height

Formula

`"V" = 1/2*(pi*"h"^2)/"p"`

Example

`"1963.495m³"=1/2*(pi*("50m")^2)/"2"`

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Volume of Paraboloid given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid
V = 1/2*(pi*h^2)/p
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Paraboloid - (Measured in Cubic Meter) - Volume of Paraboloid is the amount of three dimensional space occupied by the Paraboloid.
Height of Paraboloid - (Measured in Meter) - Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.
Shape Parameter of Paraboloid - Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid.

STEP 1: Convert Input(s) to Base Unit

Height of Paraboloid: 50 Meter --> 50 Meter No Conversion Required
Shape Parameter of Paraboloid: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/2*(pi*h^2)/p --> 1/2*(pi*50^2)/2

Evaluating ... ...

V = 1963.49540849362

STEP 3: Convert Result to Output's Unit

1963.49540849362 Cubic Meter --> No Conversion Required

FINAL ANSWER

1963.49540849362 ≈ 1963.495 Cubic Meter <-- Volume of Paraboloid

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Paraboloid » Volume and Surface to Volume Ratio of Paraboloid » Volume of Paraboloid given Height

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Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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Verified by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 5 Volume and Surface to Volume Ratio of Paraboloid Calculators

Volume of Paraboloid given Surface to Volume Ratio

Go Volume of Paraboloid = (Lateral Surface Area of Paraboloid+pi*Radius of Paraboloid^2)/Surface to Volume Ratio of Paraboloid

Volume of Paraboloid given Total Surface Area and Lateral Surface Area

Go Volume of Paraboloid = 1/2*(Total Surface Area of Paraboloid-Lateral Surface Area of Paraboloid)*Height of Paraboloid

Volume of Paraboloid given Height

Go Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid

Volume of Paraboloid given Radius

Go Volume of Paraboloid = 1/2*pi*Shape Parameter of Paraboloid*Radius of Paraboloid^4

Volume of Paraboloid

Go Volume of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid

< 4 Volume of Paraboloid Calculators

Volume of Paraboloid given Lateral Surface Area

Go Volume of Paraboloid = pi/(32*Shape Parameter of Paraboloid^3)*(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)^2

Volume of Paraboloid given Height

Go Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid

Volume of Paraboloid given Radius

Go Volume of Paraboloid = 1/2*pi*Shape Parameter of Paraboloid*Radius of Paraboloid^4

Volume of Paraboloid

Go Volume of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid

Volume of Paraboloid given Height Formula

Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid
V = 1/2*(pi*h^2)/p

What is Paraboloid?

In geometry, a Paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane section of a paraboloid by a plane parallel to the axis of symmetry is a parabola. The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines (in the case of a section by a tangent plane). The paraboloid is elliptic if every other nonempty plane section is either an ellipse, or a single point (in the case of a section by a tangent plane). A paraboloid is either elliptic or hyperbolic.

How to Calculate Volume of Paraboloid given Height?

Volume of Paraboloid given Height calculator uses Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid to calculate the Volume of Paraboloid, The Volume of Paraboloid given Height formula is defined as amount of three dimensional space occupied by Paraboloid, calculated using height of Paraboloid. Volume of Paraboloid is denoted by V symbol.

How to calculate Volume of Paraboloid given Height using this online calculator? To use this online calculator for Volume of Paraboloid given Height, enter Height of Paraboloid (h) & Shape Parameter of Paraboloid (p) and hit the calculate button. Here is how the Volume of Paraboloid given Height calculation can be explained with given input values -> 1963.495 = 1/2*(pi*50^2)/2.

FAQ

What is Volume of Paraboloid given Height?

The Volume of Paraboloid given Height formula is defined as amount of three dimensional space occupied by Paraboloid, calculated using height of Paraboloid and is represented as V = 1/2*(pi*h^2)/p or Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid. Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid & Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid.

How to calculate Volume of Paraboloid given Height?

The Volume of Paraboloid given Height formula is defined as amount of three dimensional space occupied by Paraboloid, calculated using height of Paraboloid is calculated using Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid. To calculate Volume of Paraboloid given Height, you need Height of Paraboloid (h) & Shape Parameter of Paraboloid (p). With our tool, you need to enter the respective value for Height of Paraboloid & Shape Parameter of Paraboloid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Paraboloid?

In this formula, Volume of Paraboloid uses Height of Paraboloid & Shape Parameter of Paraboloid. We can use 7 other way(s) to calculate the same, which is/are as follows -

Volume of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid
Volume of Paraboloid = 1/2*(Total Surface Area of Paraboloid-Lateral Surface Area of Paraboloid)*Height of Paraboloid
Volume of Paraboloid = (Lateral Surface Area of Paraboloid+pi*Radius of Paraboloid^2)/Surface to Volume Ratio of Paraboloid
Volume of Paraboloid = 1/2*pi*Shape Parameter of Paraboloid*Radius of Paraboloid^4
Volume of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid
Volume of Paraboloid = pi/(32*Shape Parameter of Paraboloid^3)*(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)^2
Volume of Paraboloid = 1/2*pi*Shape Parameter of Paraboloid*Radius of Paraboloid^4

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