Insphere Radius of Tetrahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3
ri = rc/3
This formula uses 2 Variables
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.
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.
STEP 1: Convert Input(s) to Base Unit
Circumsphere Radius of Tetrahedron: 6 Meter --> 6 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = rc/3 --> 6/3
Evaluating ... ...
ri = 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 00.003 seconds)

Credits

Created by Divanshi Jain
Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka
Divanshi Jain has created this Calculator and 100+ 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 200+ 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 Circumsphere Radius Formula

Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3
ri = rc/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 Insphere Radius of Tetrahedron given Circumsphere Radius?

Insphere Radius of Tetrahedron given Circumsphere Radius calculator uses Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3 to calculate the Insphere Radius of Tetrahedron, The Insphere Radius of Tetrahedron given Circumsphere Radius 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 circumsphere radius of Tetrahedron. Insphere Radius of Tetrahedron is denoted by ri symbol.

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

FAQ

What is Insphere Radius of Tetrahedron given Circumsphere Radius?
The Insphere Radius of Tetrahedron given Circumsphere Radius 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 circumsphere radius of Tetrahedron and is represented as ri = rc/3 or Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3. 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.
How to calculate Insphere Radius of Tetrahedron given Circumsphere Radius?
The Insphere Radius of Tetrahedron given Circumsphere Radius 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 circumsphere radius of Tetrahedron is calculated using Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3. To calculate Insphere Radius of Tetrahedron given Circumsphere Radius, you need Circumsphere Radius of Tetrahedron (rc). With our tool, you need to enter the respective value for Circumsphere 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 Insphere Radius of Tetrahedron?
In this formula, Insphere Radius of Tetrahedron uses Circumsphere Radius 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 = 2*sqrt(2)*Midsphere Radius of Tetrahedron/(2*sqrt(6))
  • Insphere Radius of Tetrahedron = (6*sqrt(6))/(Surface to Volume Ratio 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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