Diameter 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 Diameter of Hypersphere is twice the distance from the center to any point on the Hypersphere which is the 4D extension of sphere in 3D and circle in 2D.ⓘ Diameter of Hypersphere given Hypervolume [D]

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Formula

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Diameter of Hypersphere given Hypervolume

Formula

`"D" = 2*((2*"V"_{"Hyper"})/pi^2)^(1/4)`

Example

`"10.01274m"=2*((2*"3100m⁴")/pi^2)^(1/4)`

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Diameter of Hypersphere given Hypervolume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Hypersphere = 2*((2*Hypervolume of Hypersphere)/pi^2)^(1/4)
D = 2*((2*V_Hyper)/pi^2)^(1/4)
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Diameter of Hypersphere - (Measured in Meter) - The Diameter of Hypersphere is twice the distance from the center to any point on 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

D = 2*((2*V_Hyper)/pi^2)^(1/4) --> 2*((2*3100)/pi^2)^(1/4)

Evaluating ... ...

D = 10.0127409837406

STEP 3: Convert Result to Output's Unit

10.0127409837406 Meter --> No Conversion Required

FINAL ANSWER

10.0127409837406 ≈ 10.01274 Meter <-- Diameter 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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< 3 Diameter of Hypersphere Calculators

Diameter of Hypersphere given Surface Volume

Go Diameter of Hypersphere = (4*Surface Volume of Hypersphere/(pi^2))^(1/3)

Diameter of Hypersphere given Hypervolume

Go Diameter of Hypersphere = 2*((2*Hypervolume of Hypersphere)/pi^2)^(1/4)

Diameter of Hypersphere

Go Diameter of Hypersphere = 2*Radius of Hypersphere

Diameter of Hypersphere given Hypervolume Formula

Diameter of Hypersphere = 2*((2*Hypervolume of Hypersphere)/pi^2)^(1/4)
D = 2*((2*V_Hyper)/pi^2)^(1/4)

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 Diameter of Hypersphere given Hypervolume?

Diameter of Hypersphere given Hypervolume calculator uses Diameter of Hypersphere = 2*((2*Hypervolume of Hypersphere)/pi^2)^(1/4) to calculate the Diameter of Hypersphere, The Diameter of Hypersphere given Hypervolume formula is defined as twice the distance from the center to any point on the Hypersphere which is the 4D extension of sphere in 3D and circle in 2D, calculated using hypervolume of Hypersphere. Diameter of Hypersphere is denoted by D symbol.

How to calculate Diameter of Hypersphere given Hypervolume using this online calculator? To use this online calculator for Diameter of Hypersphere given Hypervolume, enter Hypervolume of Hypersphere (V_Hyper) and hit the calculate button. Here is how the Diameter of Hypersphere given Hypervolume calculation can be explained with given input values -> 10.01274 = 2*((2*3100)/pi^2)^(1/4).

FAQ

What is Diameter of Hypersphere given Hypervolume?

The Diameter of Hypersphere given Hypervolume formula is defined as twice the distance from the center to any point on the Hypersphere which is the 4D extension of sphere in 3D and circle in 2D, calculated using hypervolume of Hypersphere and is represented as D = 2*((2*V_Hyper)/pi^2)^(1/4) or Diameter of Hypersphere = 2*((2*Hypervolume of Hypersphere)/pi^2)^(1/4). 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 Diameter of Hypersphere given Hypervolume?

The Diameter of Hypersphere given Hypervolume formula is defined as twice the distance from the center to any point on the Hypersphere which is the 4D extension of sphere in 3D and circle in 2D, calculated using hypervolume of Hypersphere is calculated using Diameter of Hypersphere = 2*((2*Hypervolume of Hypersphere)/pi^2)^(1/4). To calculate Diameter 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 Diameter of Hypersphere?

In this formula, Diameter of Hypersphere uses Hypervolume of Hypersphere. We can use 2 other way(s) to calculate the same, which is/are as follows -

Diameter of Hypersphere = 2*Radius of Hypersphere
Diameter of Hypersphere = (4*Surface Volume of Hypersphere/(pi^2))^(1/3)

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