Midsphere 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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✖Midsphere Radius of Tetrahedron is the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere.ⓘ Midsphere Radius of Tetrahedron given Face Area [r_m]

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Midsphere Radius of Tetrahedron given Face Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(2))
r_m = sqrt((4*A_Face)/sqrt(3))/(2*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

Midsphere Radius of Tetrahedron - (Measured in Meter) - Midsphere Radius of Tetrahedron is the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that 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_m = sqrt((4*A_Face)/sqrt(3))/(2*sqrt(2)) --> sqrt((4*45)/sqrt(3))/(2*sqrt(2))

Evaluating ... ...

r_m = 3.60421712120213

STEP 3: Convert Result to Output's Unit

3.60421712120213 Meter --> No Conversion Required

FINAL ANSWER

3.60421712120213 ≈ 3.604217 Meter <-- Midsphere Radius of Tetrahedron

(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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< Midsphere Radius of Tetrahedron Calculators

Midsphere Radius of Tetrahedron given Total Surface Area

LaTeX Go Midsphere Radius of Tetrahedron = sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))/(2*sqrt(2))

Midsphere Radius of Tetrahedron given Face Area

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

Midsphere Radius of Tetrahedron given Circumsphere Radius

LaTeX Go Midsphere Radius of Tetrahedron = sqrt(1/3)*Circumsphere Radius of Tetrahedron

Midsphere Radius of Tetrahedron

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

Midsphere Radius of Tetrahedron given Face Area Formula

LaTeX Go

Midsphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(2))
r_m = sqrt((4*A_Face)/sqrt(3))/(2*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 Midsphere Radius of Tetrahedron given Face Area?

Midsphere Radius of Tetrahedron given Face Area calculator uses Midsphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(2)) to calculate the Midsphere Radius of Tetrahedron, The Midsphere Radius of Tetrahedron given Face Area formula is defined as the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere, calculated using face area of Tetrahedron. Midsphere Radius of Tetrahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Tetrahedron given Face Area using this online calculator? To use this online calculator for Midsphere Radius of Tetrahedron given Face Area, enter Face Area of Tetrahedron (A_Face) and hit the calculate button. Here is how the Midsphere Radius of Tetrahedron given Face Area calculation can be explained with given input values -> 3.604217 = sqrt((4*45)/sqrt(3))/(2*sqrt(2)).

FAQ

What is Midsphere Radius of Tetrahedron given Face Area?

The Midsphere Radius of Tetrahedron given Face Area formula is defined as the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere, calculated using face area of Tetrahedron and is represented as r_m = sqrt((4*A_Face)/sqrt(3))/(2*sqrt(2)) or Midsphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(2)). Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.

How to calculate Midsphere Radius of Tetrahedron given Face Area?

The Midsphere Radius of Tetrahedron given Face Area formula is defined as the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere, calculated using face area of Tetrahedron is calculated using Midsphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(2)). To calculate Midsphere 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 Midsphere Radius of Tetrahedron?

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

Midsphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(2))
Midsphere Radius of Tetrahedron = sqrt(1/3)*Circumsphere Radius of Tetrahedron
Midsphere Radius of Tetrahedron = sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))/(2*sqrt(2))

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