Height of Tetrahedron given Volume Calculator

✖Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.ⓘ Height of Tetrahedron given Volume [h]

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Formula

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Height of Tetrahedron given Volume

Formula

`"h" = sqrt(2/3)*(6*sqrt(2)*"V")^(1/3)`

Example

`"8.214293m"=sqrt(2/3)*(6*sqrt(2)*"120m³")^(1/3)`

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Height of Tetrahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)
h = sqrt(2/3)*(6*sqrt(2)*V)^(1/3)
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

Height of Tetrahedron - (Measured in Meter) - Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.
Volume of Tetrahedron - (Measured in Cubic Meter) - Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Tetrahedron: 120 Cubic Meter --> 120 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(2/3)*(6*sqrt(2)*V)^(1/3) --> sqrt(2/3)*(6*sqrt(2)*120)^(1/3)

Evaluating ... ...

h = 8.21429322730446

STEP 3: Convert Result to Output's Unit

8.21429322730446 Meter --> No Conversion Required

FINAL ANSWER

8.21429322730446 ≈ 8.214293 Meter <-- Height of Tetrahedron

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

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

Dhruv Walia has created this Calculator and 1100+ more calculators!

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Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

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< 8 Height of Tetrahedron Calculators

Height of Tetrahedron given Total Surface Area

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

Height of Tetrahedron given Volume

Go Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)

Height of Tetrahedron given Face Area

Go Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))

Height of Tetrahedron given Midsphere Radius

Go Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron

Height of Tetrahedron

Go Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron

Height of Tetrahedron given Surface to Volume Ratio

Go Height of Tetrahedron = 12/Surface to Volume Ratio of Tetrahedron

Height of Tetrahedron given Circumsphere Radius

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

Height of Tetrahedron given Insphere Radius

Go Height of Tetrahedron = 4*Insphere Radius of Tetrahedron

< 4 Height of Tetrahedron Calculators

Height of Tetrahedron given Volume

Go Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)

Height of Tetrahedron given Face Area

Go Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))

Height of Tetrahedron

Go Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron

Height of Tetrahedron given Circumsphere Radius

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

Height of Tetrahedron given Volume Formula

Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)
h = sqrt(2/3)*(6*sqrt(2)*V)^(1/3)

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 Height of Tetrahedron given Volume?

Height of Tetrahedron given Volume calculator uses Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3) to calculate the Height of Tetrahedron, The Height of Tetrahedron given Volume formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the volume of the Tetrahedron. Height of Tetrahedron is denoted by h symbol.

How to calculate Height of Tetrahedron given Volume using this online calculator? To use this online calculator for Height of Tetrahedron given Volume, enter Volume of Tetrahedron (V) and hit the calculate button. Here is how the Height of Tetrahedron given Volume calculation can be explained with given input values -> 8.214293 = sqrt(2/3)*(6*sqrt(2)*120)^(1/3).

FAQ

What is Height of Tetrahedron given Volume?

The Height of Tetrahedron given Volume formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the volume of the Tetrahedron and is represented as h = sqrt(2/3)*(6*sqrt(2)*V)^(1/3) or Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3). Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.

How to calculate Height of Tetrahedron given Volume?

The Height of Tetrahedron given Volume formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the volume of the Tetrahedron is calculated using Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3). To calculate Height of Tetrahedron given Volume, you need Volume of Tetrahedron (V). With our tool, you need to enter the respective value for Volume 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 Height of Tetrahedron?

In this formula, Height of Tetrahedron uses Volume of Tetrahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -

Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron
Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron
Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))
Height of Tetrahedron = 4*Insphere Radius of Tetrahedron
Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron
Height of Tetrahedron = 12/Surface to Volume Ratio of Tetrahedron
Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3)))
Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron
Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron
Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))

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