Insphere Radius of Tetrahedron given Face Area Calculator

✖Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.ⓘ Face Area of Tetrahedron [A_Face]

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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 Face Area [r_i]

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Insphere Radius of Tetrahedron given Face Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6))
r_i = sqrt((4*A_Face)/sqrt(3))/(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.
Face Area of Tetrahedron - (Measured in Square Meter) - Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.

STEP 1: Convert Input(s) to Base Unit

Face Area of Tetrahedron: 45 Square Meter --> 45 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = sqrt((4*A_Face)/sqrt(3))/(2*sqrt(6)) --> sqrt((4*45)/sqrt(3))/(2*sqrt(6))

Evaluating ... ...

r_i = 2.08089572514391

STEP 3: Convert Result to Output's Unit

2.08089572514391 Meter --> No Conversion Required

FINAL ANSWER

2.08089572514391 ≈ 2.080896 Meter <-- Insphere Radius of Tetrahedron

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Insphere Radius of Tetrahedron Calculators

Insphere Radius of Tetrahedron given Face Area

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

Insphere Radius of Tetrahedron

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

Insphere Radius of Tetrahedron given Circumsphere Radius

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

Insphere Radius of Tetrahedron given Height

LaTeX Go Insphere Radius of Tetrahedron = Height of Tetrahedron/4

< Radius of Tetrahedron Calculators

Insphere Radius of Tetrahedron given Face Area

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

Circumsphere Radius of Tetrahedron

LaTeX Go Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*Edge Length of Tetrahedron

Midsphere Radius of Tetrahedron

LaTeX Go Midsphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(2))

Insphere Radius of Tetrahedron

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

Insphere Radius of Tetrahedron given Face Area Formula

LaTeX Go

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

Insphere Radius of Tetrahedron given Face Area calculator uses Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6)) to calculate the Insphere Radius of Tetrahedron, Insphere Radius of Tetrahedron given Face Area 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, and calculated using the face area of the Tetrahedron. Insphere Radius of Tetrahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Tetrahedron given Face Area using this online calculator? To use this online calculator for Insphere Radius of Tetrahedron given Face Area, enter Face Area of Tetrahedron (A_Face) and hit the calculate button. Here is how the Insphere Radius of Tetrahedron given Face Area calculation can be explained with given input values -> 2.080896 = sqrt((4*45)/sqrt(3))/(2*sqrt(6)).

FAQ

What is Insphere Radius of Tetrahedron given Face Area?

Insphere Radius of Tetrahedron given Face Area 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, and calculated using the face area of the Tetrahedron and is represented as r_i = sqrt((4*A_Face)/sqrt(3))/(2*sqrt(6)) or Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6)). Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.

How to calculate Insphere Radius of Tetrahedron given Face Area?

Insphere Radius of Tetrahedron given Face Area 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, and calculated using the face area of the Tetrahedron is calculated using Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6)). To calculate Insphere Radius of Tetrahedron given Face Area, you need Face Area of Tetrahedron (A_Face). With our tool, you need to enter the respective value for Face Area 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 Face Area of Tetrahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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