Insphere Radius of Tetrahedron given Surface to Volume Ratio Calculator

✖The Surface to Volume Ratio of Tetrahedron is the numerical ratio of the total surface area to the volume of the Tetrahedron.ⓘ Surface to Volume Ratio of Tetrahedron [R_A/V]

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✖Insphere Radius of Tetrahedron is the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere.ⓘ Insphere Radius of Tetrahedron given Surface to Volume Ratio [r_i]

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Formula

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Insphere Radius of Tetrahedron given Surface to Volume Ratio

Formula

`"r"_{"i"} = (6*sqrt(6))/("R"_{"A/V"}*(2*sqrt(6)))`

Example

`"2m"=(6*sqrt(6))/("1.5m⁻¹"*(2*sqrt(6)))`

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Insphere Radius of Tetrahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Tetrahedron = (6*sqrt(6))/(Surface to Volume Ratio of Tetrahedron*(2*sqrt(6)))
r_i = (6*sqrt(6))/(R_A/V*(2*sqrt(6)))
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Insphere Radius of Tetrahedron - (Measured in Meter) - Insphere Radius of Tetrahedron is the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere.
Surface to Volume Ratio of Tetrahedron - (Measured in 1 per Meter) - The Surface to Volume Ratio of Tetrahedron is the numerical ratio of the total surface area to the volume of the Tetrahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Tetrahedron: 1.5 1 per Meter --> 1.5 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (6*sqrt(6))/(R_A/V*(2*sqrt(6))) --> (6*sqrt(6))/(1.5*(2*sqrt(6)))

Evaluating ... ...

r_i = 2

STEP 3: Convert Result to Output's Unit

2 Meter --> No Conversion Required

FINAL ANSWER

2 Meter <-- Insphere Radius of Tetrahedron

(Calculation completed in 00.004 seconds)

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Credits

Created by Divanshi Jain

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

Divanshi Jain has created this Calculator and 300+ more calculators!

Verified by Dhruv Walia

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

Dhruv Walia has verified this Calculator and 400+ more calculators!

< 8 Insphere Radius of Tetrahedron Calculators

Insphere Radius of Tetrahedron given Total Surface Area

Go Insphere Radius of Tetrahedron = sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))/(2*sqrt(6))

Insphere Radius of Tetrahedron given Face Area

Go Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6))

Insphere Radius of Tetrahedron given Surface to Volume Ratio

Go Insphere Radius of Tetrahedron = (6*sqrt(6))/(Surface to Volume Ratio of Tetrahedron*(2*sqrt(6)))

Insphere Radius of Tetrahedron given Midsphere Radius

Go Insphere Radius of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron/(2*sqrt(6))

Insphere Radius of Tetrahedron given Volume

Go Insphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(6))

Insphere Radius of Tetrahedron

Go Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6))

Insphere Radius of Tetrahedron given Circumsphere Radius

Go Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3

Insphere Radius of Tetrahedron given Height

Go Insphere Radius of Tetrahedron = Height of Tetrahedron/4

Insphere Radius of Tetrahedron given Surface to Volume Ratio Formula

Insphere Radius of Tetrahedron = (6*sqrt(6))/(Surface to Volume Ratio of Tetrahedron*(2*sqrt(6)))
r_i = (6*sqrt(6))/(R_A/V*(2*sqrt(6)))

What is a Tetrahedron?

A Tetrahedron is a symmetric and closed three dimensional shape with 4 identical equilateral triangular faces. It is a Platonic solid, which has 4 faces, 4 vertices and 6 edges. At each vertex, three equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Insphere Radius of Tetrahedron given Surface to Volume Ratio?

Insphere Radius of Tetrahedron given Surface to Volume Ratio calculator uses Insphere Radius of Tetrahedron = (6*sqrt(6))/(Surface to Volume Ratio of Tetrahedron*(2*sqrt(6))) to calculate the Insphere Radius of Tetrahedron, The Insphere Radius of Tetrahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Tetrahedron. Insphere Radius of Tetrahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Tetrahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Insphere Radius of Tetrahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Tetrahedron (R_A/V) and hit the calculate button. Here is how the Insphere Radius of Tetrahedron given Surface to Volume Ratio calculation can be explained with given input values -> 2 = (6*sqrt(6))/(1.5*(2*sqrt(6))).

FAQ

What is Insphere Radius of Tetrahedron given Surface to Volume Ratio?

The Insphere Radius of Tetrahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Tetrahedron and is represented as r_i = (6*sqrt(6))/(R_A/V*(2*sqrt(6))) or Insphere Radius of Tetrahedron = (6*sqrt(6))/(Surface to Volume Ratio of Tetrahedron*(2*sqrt(6))). The Surface to Volume Ratio of Tetrahedron is the numerical ratio of the total surface area to the volume of the Tetrahedron.

How to calculate Insphere Radius of Tetrahedron given Surface to Volume Ratio?

The Insphere Radius of Tetrahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Tetrahedron is calculated using Insphere Radius of Tetrahedron = (6*sqrt(6))/(Surface to Volume Ratio of Tetrahedron*(2*sqrt(6))). To calculate Insphere Radius of Tetrahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Tetrahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Tetrahedron 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 Insphere Radius of Tetrahedron?

In this formula, Insphere Radius of Tetrahedron uses Surface to Volume Ratio of Tetrahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6))
Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6))
Insphere Radius of Tetrahedron = Height of Tetrahedron/4
Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3
Insphere Radius of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron/(2*sqrt(6))
Insphere Radius of Tetrahedron = sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))/(2*sqrt(6))
Insphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(6))

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