Volume of Tetrahedron given Insphere Radius Calculator

✖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 [r_i]

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✖Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.ⓘ Volume of Tetrahedron given Insphere Radius [V]

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Volume of Tetrahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Tetrahedron = ((2*sqrt(6)*Insphere Radius of Tetrahedron)^3)/(6*sqrt(2))
V = ((2*sqrt(6)*r_i)^3)/(6*sqrt(2))
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

Volume of Tetrahedron - (Measured in Cubic Meter) - Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.
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.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Tetrahedron: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = ((2*sqrt(6)*r_i)^3)/(6*sqrt(2)) --> ((2*sqrt(6)*2)^3)/(6*sqrt(2))

Evaluating ... ...

V = 110.851251684408

STEP 3: Convert Result to Output's Unit

110.851251684408 Cubic Meter --> No Conversion Required

FINAL ANSWER

110.851251684408 ≈ 110.8513 Cubic Meter <-- Volume of Tetrahedron

(Calculation completed in 00.004 seconds)

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

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< Volume of Tetrahedron Calculators

Volume of Tetrahedron given Surface to Volume Ratio

LaTeX Go Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron given Circumsphere Radius

LaTeX Go Volume of Tetrahedron = ((2*sqrt(2/3)*Circumsphere Radius of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron given Total Surface Area

LaTeX Go Volume of Tetrahedron = sqrt(2)/12*(Total Surface Area of Tetrahedron/sqrt(3))^(3/2)

Volume of Tetrahedron

LaTeX Go Volume of Tetrahedron = (Edge Length of Tetrahedron^3)/(6*sqrt(2))

Volume of Tetrahedron given Insphere Radius Formula

LaTeX Go

Volume of Tetrahedron = ((2*sqrt(6)*Insphere Radius of Tetrahedron)^3)/(6*sqrt(2))
V = ((2*sqrt(6)*r_i)^3)/(6*sqrt(2))

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 Volume of Tetrahedron given Insphere Radius?

Volume of Tetrahedron given Insphere Radius calculator uses Volume of Tetrahedron = ((2*sqrt(6)*Insphere Radius of Tetrahedron)^3)/(6*sqrt(2)) to calculate the Volume of Tetrahedron, The Volume of Tetrahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron. Volume of Tetrahedron is denoted by V symbol.

How to calculate Volume of Tetrahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Tetrahedron given Insphere Radius, enter Insphere Radius of Tetrahedron (r_i) and hit the calculate button. Here is how the Volume of Tetrahedron given Insphere Radius calculation can be explained with given input values -> 110.8513 = ((2*sqrt(6)*2)^3)/(6*sqrt(2)).

FAQ

What is Volume of Tetrahedron given Insphere Radius?

The Volume of Tetrahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron and is represented as V = ((2*sqrt(6)*r_i)^3)/(6*sqrt(2)) or Volume of Tetrahedron = ((2*sqrt(6)*Insphere Radius of Tetrahedron)^3)/(6*sqrt(2)). 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.

How to calculate Volume of Tetrahedron given Insphere Radius?

The Volume of Tetrahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron is calculated using Volume of Tetrahedron = ((2*sqrt(6)*Insphere Radius of Tetrahedron)^3)/(6*sqrt(2)). To calculate Volume of Tetrahedron given Insphere Radius, you need Insphere Radius of Tetrahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius 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 Volume of Tetrahedron?

In this formula, Volume of Tetrahedron uses Insphere Radius of Tetrahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Tetrahedron = (Edge Length of Tetrahedron^3)/(6*sqrt(2))
Volume of Tetrahedron = sqrt(2)/12*(Total Surface Area of Tetrahedron/sqrt(3))^(3/2)
Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2))

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