Total Surface Area of Tetrahedron given Insphere Radius Calculator

✖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 [r_i]

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✖Total Surface Area of Tetrahedron is the total quantity of plane enclosed by the entire surface of the Tetrahedron.ⓘ Total Surface Area of Tetrahedron given Insphere Radius [TSA]

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Total Surface Area of Tetrahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(6)*Insphere Radius of Tetrahedron)^2
TSA = sqrt(3)*(2*sqrt(6)*r_i)^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

Total Surface Area of Tetrahedron - (Measured in Square Meter) - Total Surface Area of Tetrahedron is the total quantity of plane enclosed by the entire surface of the Tetrahedron.
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.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Tetrahedron: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = sqrt(3)*(2*sqrt(6)*r_i)^2 --> sqrt(3)*(2*sqrt(6)*2)^2

Evaluating ... ...

TSA = 166.276877526612

STEP 3: Convert Result to Output's Unit

166.276877526612 Square Meter --> No Conversion Required

FINAL ANSWER

166.276877526612 ≈ 166.2769 Square Meter <-- Total Surface Area of Tetrahedron

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Total Surface Area of Tetrahedron Calculators

Total Surface Area of Tetrahedron given Circumsphere Radius

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

Total Surface Area of Tetrahedron given Volume

LaTeX Go Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3)

Total Surface Area of Tetrahedron given Height

LaTeX Go Total Surface Area of Tetrahedron = sqrt(3)*(sqrt(3/2)*Height of Tetrahedron)^2

Total Surface Area of Tetrahedron

LaTeX Go Total Surface Area of Tetrahedron = sqrt(3)*Edge Length of Tetrahedron^2

Total Surface Area of Tetrahedron given Insphere Radius Formula

LaTeX Go

Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(6)*Insphere Radius of Tetrahedron)^2
TSA = sqrt(3)*(2*sqrt(6)*r_i)^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 Total Surface Area of Tetrahedron given Insphere Radius?

Total Surface Area of Tetrahedron given Insphere Radius calculator uses Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(6)*Insphere Radius of Tetrahedron)^2 to calculate the Total Surface Area of Tetrahedron, The Total Surface Area of Tetrahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron. Total Surface Area of Tetrahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Tetrahedron given Insphere Radius using this online calculator? To use this online calculator for Total Surface Area of Tetrahedron given Insphere Radius, enter Insphere Radius of Tetrahedron (r_i) and hit the calculate button. Here is how the Total Surface Area of Tetrahedron given Insphere Radius calculation can be explained with given input values -> 166.2769 = sqrt(3)*(2*sqrt(6)*2)^2.

FAQ

What is Total Surface Area of Tetrahedron given Insphere Radius?

The Total Surface Area of Tetrahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron and is represented as TSA = sqrt(3)*(2*sqrt(6)*r_i)^2 or Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(6)*Insphere Radius of Tetrahedron)^2. 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.

How to calculate Total Surface Area of Tetrahedron given Insphere Radius?

The Total Surface Area of Tetrahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron is calculated using Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(6)*Insphere Radius of Tetrahedron)^2. To calculate Total Surface Area of Tetrahedron given Insphere Radius, you need Insphere Radius of Tetrahedron (r_i). With our tool, you need to enter the respective value for Insphere 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 Total Surface Area of Tetrahedron?

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

Total Surface Area of Tetrahedron = sqrt(3)*Edge Length of Tetrahedron^2
Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3)
Total Surface Area of Tetrahedron = sqrt(3)*(sqrt(3/2)*Height of Tetrahedron)^2

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