## Circumsphere Radius of Tetrahedron given Face Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt((4*Face Area of Tetrahedron)/sqrt(3))
rc = 1/2*sqrt(3/2)*sqrt((4*AFace)/sqrt(3))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Circumsphere Radius of Tetrahedron - (Measured in Meter) - Circumsphere Radius of Tetrahedron is the radius of the sphere that contains the Tetrahedron in such a way that all the vertices are lying on 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
rc = 1/2*sqrt(3/2)*sqrt((4*AFace)/sqrt(3)) --> 1/2*sqrt(3/2)*sqrt((4*45)/sqrt(3))
Evaluating ... ...
rc = 6.24268717543173
STEP 3: Convert Result to Output's Unit
6.24268717543173 Meter --> No Conversion Required
6.24268717543173 6.242687 Meter <-- Circumsphere Radius of Tetrahedron
(Calculation completed in 00.004 seconds)
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Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka
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## < 8 Circumsphere Radius of Tetrahedron Calculators

Circumsphere Radius of Tetrahedron given Total Surface Area
Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))
Circumsphere Radius of Tetrahedron given Face Area
Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt((4*Face Area of Tetrahedron)/sqrt(3))
Circumsphere Radius of Tetrahedron given Volume
Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)
Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*Edge Length of Tetrahedron
Circumsphere Radius of Tetrahedron given Surface to Volume Ratio
Circumsphere Radius of Tetrahedron = 9/Surface to Volume Ratio of Tetrahedron
Circumsphere Radius of Tetrahedron given Height
Circumsphere Radius of Tetrahedron = 3/4*Height of Tetrahedron

## Circumsphere Radius of Tetrahedron given Face Area Formula

Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt((4*Face Area of Tetrahedron)/sqrt(3))
rc = 1/2*sqrt(3/2)*sqrt((4*AFace)/sqrt(3))

## 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 Circumsphere Radius of Tetrahedron given Face Area?

Circumsphere Radius of Tetrahedron given Face Area calculator uses Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt((4*Face Area of Tetrahedron)/sqrt(3)) to calculate the Circumsphere Radius of Tetrahedron, The Circumsphere Radius of Tetrahedron given Face Area formula is defined as the radius of the sphere that contains the Tetrahedron in such a way that all the vertices are lying on the sphere, calculated using face area of Tetrahedron. Circumsphere Radius of Tetrahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Tetrahedron given Face Area using this online calculator? To use this online calculator for Circumsphere Radius of Tetrahedron given Face Area, enter Face Area of Tetrahedron (AFace) and hit the calculate button. Here is how the Circumsphere Radius of Tetrahedron given Face Area calculation can be explained with given input values -> 6.242687 = 1/2*sqrt(3/2)*sqrt((4*45)/sqrt(3)).

### FAQ

What is Circumsphere Radius of Tetrahedron given Face Area?
The Circumsphere Radius of Tetrahedron given Face Area formula is defined as the radius of the sphere that contains the Tetrahedron in such a way that all the vertices are lying on the sphere, calculated using face area of Tetrahedron and is represented as rc = 1/2*sqrt(3/2)*sqrt((4*AFace)/sqrt(3)) or Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt((4*Face Area of Tetrahedron)/sqrt(3)). Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.
How to calculate Circumsphere Radius of Tetrahedron given Face Area?
The Circumsphere Radius of Tetrahedron given Face Area formula is defined as the radius of the sphere that contains the Tetrahedron in such a way that all the vertices are lying on the sphere, calculated using face area of Tetrahedron is calculated using Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt((4*Face Area of Tetrahedron)/sqrt(3)). To calculate Circumsphere Radius of Tetrahedron given Face Area, you need Face Area of Tetrahedron (AFace). 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 Circumsphere Radius of Tetrahedron?
In this formula, Circumsphere Radius of Tetrahedron uses Face Area of Tetrahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -
• Circumsphere Radius of Tetrahedron = 3/4*Height of Tetrahedron
• Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*Edge Length of Tetrahedron
• Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))
• Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)