Hypervolume of Hypersphere given Surface Volume Calculator

✖The Surface Volume of Hypersphere is the volume of the surface of the Hypersphere which is the 4D extension of sphere in 3D and circle in 2D.ⓘ Surface Volume of Hypersphere [V_Surface]

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✖The Hypervolume of Hypersphere is the 4-dimensional volume of the 4D object Hypersphere which is the 4D extension of the sphere in 3D and a circle in 2D.ⓘ Hypervolume of Hypersphere given Surface Volume [V_Hyper]

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Formula

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Hypervolume of Hypersphere given Surface Volume

Formula

`"V"_{"Hyper"} = pi^2/2*("V"_{"Surface"}/(2*pi^2))^(4/3)`

Example

`"3138.702m⁴"=pi^2/2*("2500m³"/(2*pi^2))^(4/3)`

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Hypervolume of Hypersphere given Surface Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hypervolume of Hypersphere = pi^2/2*(Surface Volume of Hypersphere/(2*pi^2))^(4/3)
V_Hyper = pi^2/2*(V_Surface/(2*pi^2))^(4/3)
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Hypervolume of Hypersphere - (Measured in Meter⁴) - The Hypervolume of Hypersphere is the 4-dimensional volume of the 4D object Hypersphere which is the 4D extension of the sphere in 3D and a circle in 2D.
Surface Volume of Hypersphere - (Measured in Cubic Meter) - The Surface Volume of Hypersphere is the volume of the surface of the Hypersphere which is the 4D extension of sphere in 3D and circle in 2D.

STEP 1: Convert Input(s) to Base Unit

Surface Volume of Hypersphere: 2500 Cubic Meter --> 2500 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_Hyper = pi^2/2*(V_Surface/(2*pi^2))^(4/3) --> pi^2/2*(2500/(2*pi^2))^(4/3)

Evaluating ... ...

V_Hyper = 3138.70216203902

STEP 3: Convert Result to Output's Unit

3138.70216203902 Meter⁴ --> No Conversion Required

FINAL ANSWER

3138.70216203902 ≈ 3138.702 Meter⁴ <-- Hypervolume of Hypersphere

(Calculation completed in 00.020 seconds)

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Created by Divanshi Jain

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

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

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< 2 Hypervolume of Hypersphere Calculators

Hypervolume of Hypersphere given Surface Volume

Go Hypervolume of Hypersphere = pi^2/2*(Surface Volume of Hypersphere/(2*pi^2))^(4/3)

Hypervolume of Hypersphere

Go Hypervolume of Hypersphere = ((pi^2)/2)*(Radius of Hypersphere^4)

Hypervolume of Hypersphere given Surface Volume Formula

Hypervolume of Hypersphere = pi^2/2*(Surface Volume of Hypersphere/(2*pi^2))^(4/3)
V_Hyper = pi^2/2*(V_Surface/(2*pi^2))^(4/3)

What is a Hypersphere?

Hypersphere is basically the sphere in 4th dimension. This is the expansion of circle (2D) and sphere (3D) into a fourth dimension of space. This doesn't exist in our three-dimensional world, but calculations regarding Hyperspheres can easily be done by extending the formulas of 3D sphere into 4D.

How to Calculate Hypervolume of Hypersphere given Surface Volume?

Hypervolume of Hypersphere given Surface Volume calculator uses Hypervolume of Hypersphere = pi^2/2*(Surface Volume of Hypersphere/(2*pi^2))^(4/3) to calculate the Hypervolume of Hypersphere, The Hypervolume of Hypersphere given Surface Volume formula is defined as the 4-dimensional volume of the 4D object Hypersphere which is the 4D extension of the sphere in 3D and a circle in 2D, calculated using surface volume of Hypersphere. Hypervolume of Hypersphere is denoted by V_Hyper symbol.

How to calculate Hypervolume of Hypersphere given Surface Volume using this online calculator? To use this online calculator for Hypervolume of Hypersphere given Surface Volume, enter Surface Volume of Hypersphere (V_Surface) and hit the calculate button. Here is how the Hypervolume of Hypersphere given Surface Volume calculation can be explained with given input values -> 3138.702 = pi^2/2*(2500/(2*pi^2))^(4/3).

FAQ

What is Hypervolume of Hypersphere given Surface Volume?

The Hypervolume of Hypersphere given Surface Volume formula is defined as the 4-dimensional volume of the 4D object Hypersphere which is the 4D extension of the sphere in 3D and a circle in 2D, calculated using surface volume of Hypersphere and is represented as V_Hyper = pi^2/2*(V_Surface/(2*pi^2))^(4/3) or Hypervolume of Hypersphere = pi^2/2*(Surface Volume of Hypersphere/(2*pi^2))^(4/3). The Surface Volume of Hypersphere is the volume of the surface of the Hypersphere which is the 4D extension of sphere in 3D and circle in 2D.

How to calculate Hypervolume of Hypersphere given Surface Volume?

The Hypervolume of Hypersphere given Surface Volume formula is defined as the 4-dimensional volume of the 4D object Hypersphere which is the 4D extension of the sphere in 3D and a circle in 2D, calculated using surface volume of Hypersphere is calculated using Hypervolume of Hypersphere = pi^2/2*(Surface Volume of Hypersphere/(2*pi^2))^(4/3). To calculate Hypervolume of Hypersphere given Surface Volume, you need Surface Volume of Hypersphere (V_Surface). With our tool, you need to enter the respective value for Surface Volume of Hypersphere 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 Hypervolume of Hypersphere?

In this formula, Hypervolume of Hypersphere uses Surface Volume of Hypersphere. We can use 1 other way(s) to calculate the same, which is/are as follows -

Hypervolume of Hypersphere = ((pi^2)/2)*(Radius of Hypersphere^4)

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