Surface Volume of Hypersphere given Hypervolume Calculator

✖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 [V_Hyper]

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✖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 given Hypervolume [V_Surface]

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Formula

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Surface Volume of Hypersphere given Hypervolume

Formula

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

Example

`"2476.844m³"=2*pi^2*((2*"3100m⁴")/pi^2)^(3/4)`

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Surface Volume of Hypersphere given Hypervolume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Hypervolume of Hypersphere: 3100 Meter⁴ --> 3100 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_Surface = 2*pi^2*((2*V_Hyper)/pi^2)^(3/4) --> 2*pi^2*((2*3100)/pi^2)^(3/4)

Evaluating ... ...

V_Surface = 2476.84425675966

STEP 3: Convert Result to Output's Unit

2476.84425675966 Cubic Meter --> No Conversion Required

FINAL ANSWER

2476.84425675966 ≈ 2476.844 Cubic Meter <-- Surface Volume of Hypersphere

(Calculation completed in 00.004 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 Surface Volume of Hypersphere Calculators

Surface Volume of Hypersphere given Hypervolume

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

Surface Volume of Hypersphere

Go Surface Volume of Hypersphere = (2*(pi^2))*(Radius of Hypersphere^3)

Surface Volume of Hypersphere given Hypervolume Formula

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

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 Surface Volume of Hypersphere given Hypervolume?

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

How to calculate Surface Volume of Hypersphere given Hypervolume using this online calculator? To use this online calculator for Surface Volume of Hypersphere given Hypervolume, enter Hypervolume of Hypersphere (V_Hyper) and hit the calculate button. Here is how the Surface Volume of Hypersphere given Hypervolume calculation can be explained with given input values -> 2476.844 = 2*pi^2*((2*3100)/pi^2)^(3/4).

FAQ

What is Surface Volume of Hypersphere given Hypervolume?

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

How to calculate Surface Volume of Hypersphere given Hypervolume?

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

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

Surface Volume of Hypersphere = (2*(pi^2))*(Radius of Hypersphere^3)

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