Circumsphere Radius of Tetrahedron given Midsphere Radius Calculator

✖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 [r_m]

+10%

-10%

✖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.ⓘ Circumsphere Radius of Tetrahedron given Midsphere Radius [r_c]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Tetrahedron Formula PDF PDF Image

Circumsphere Radius of Tetrahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Tetrahedron = sqrt(3)*Midsphere Radius of Tetrahedron
r_c = sqrt(3)*r_m
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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Tetrahedron: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(3)*r_m --> sqrt(3)*4

Evaluating ... ...

r_c = 6.92820323027551

STEP 3: Convert Result to Output's Unit

6.92820323027551 Meter --> No Conversion Required

FINAL ANSWER

6.92820323027551 ≈ 6.928203 Meter <-- Circumsphere Radius of Tetrahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Platonic Solids » Tetrahedron » Radius of Tetrahedron » Circumsphere Radius of Tetrahedron » Circumsphere Radius of Tetrahedron given Midsphere Radius

Credits

Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

Divanshi Jain has created this Calculator and 300+ 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 400+ more calculators!

< Circumsphere Radius of Tetrahedron Calculators

Circumsphere Radius of Tetrahedron given Total Surface Area

LaTeX Go Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))

Circumsphere Radius of Tetrahedron given Face Area

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

Circumsphere Radius of Tetrahedron

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

Circumsphere Radius of Tetrahedron given Height

LaTeX Go Circumsphere Radius of Tetrahedron = 3/4*Height of Tetrahedron

Circumsphere Radius of Tetrahedron given Midsphere Radius Formula

LaTeX Go

Circumsphere Radius of Tetrahedron = sqrt(3)*Midsphere Radius of Tetrahedron
r_c = sqrt(3)*r_m

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 Midsphere Radius?

Circumsphere Radius of Tetrahedron given Midsphere Radius calculator uses Circumsphere Radius of Tetrahedron = sqrt(3)*Midsphere Radius of Tetrahedron to calculate the Circumsphere Radius of Tetrahedron, The Circumsphere Radius of Tetrahedron given Midsphere Radius 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 Midphere radius of Tetrahedron. Circumsphere Radius of Tetrahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Tetrahedron given Midsphere Radius using this online calculator? To use this online calculator for Circumsphere Radius of Tetrahedron given Midsphere Radius, enter Midsphere Radius of Tetrahedron (r_m) and hit the calculate button. Here is how the Circumsphere Radius of Tetrahedron given Midsphere Radius calculation can be explained with given input values -> 6.928203 = sqrt(3)*4.

FAQ

What is Circumsphere Radius of Tetrahedron given Midsphere Radius?

The Circumsphere Radius of Tetrahedron given Midsphere Radius 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 Midphere radius of Tetrahedron and is represented as r_c = sqrt(3)*r_m or Circumsphere Radius of Tetrahedron = sqrt(3)*Midsphere Radius of Tetrahedron. 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.

How to calculate Circumsphere Radius of Tetrahedron given Midsphere Radius?

The Circumsphere Radius of Tetrahedron given Midsphere Radius 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 Midphere radius of Tetrahedron is calculated using Circumsphere Radius of Tetrahedron = sqrt(3)*Midsphere Radius of Tetrahedron. To calculate Circumsphere Radius of Tetrahedron given Midsphere Radius, you need Midsphere Radius of Tetrahedron (r_m). With our tool, you need to enter the respective value for Midsphere 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 Circumsphere Radius of Tetrahedron?

In this formula, Circumsphere Radius of Tetrahedron uses Midsphere Radius of Tetrahedron. We can use 3 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((4*Face Area of Tetrahedron)/sqrt(3))

Home

FREE PDFs

🔍 Search