Volume of Tetrahedron given Height 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 [h]

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✖Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.ⓘ Volume of Tetrahedron given Height [V]

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Volume of Tetrahedron given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Height of Tetrahedron: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = ((sqrt(3/2)*h)^3)/(6*sqrt(2)) --> ((sqrt(3/2)*8)^3)/(6*sqrt(2))

Evaluating ... ...

V = 110.851251684408

STEP 3: Convert Result to Output's Unit

110.851251684408 Cubic Meter --> No Conversion Required

FINAL ANSWER

110.851251684408 ≈ 110.8513 Cubic Meter <-- Volume of Tetrahedron

(Calculation completed in 00.020 seconds)

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

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< Volume of Tetrahedron Calculators

Volume of Tetrahedron given Surface to Volume Ratio

LaTeX Go Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron given Circumsphere Radius

LaTeX Go Volume of Tetrahedron = ((2*sqrt(2/3)*Circumsphere Radius of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron given Total Surface Area

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

Volume of Tetrahedron

LaTeX Go Volume of Tetrahedron = (Edge Length of Tetrahedron^3)/(6*sqrt(2))

< Volume of Tetrahedron Calculators

Volume of Tetrahedron given Total Surface Area

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

Volume of Tetrahedron given Face Area

LaTeX Go Volume of Tetrahedron = (((4*Face Area of Tetrahedron)/sqrt(3))^(3/2))/(6*sqrt(2))

Volume of Tetrahedron given Height

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

Volume of Tetrahedron

LaTeX Go Volume of Tetrahedron = (Edge Length of Tetrahedron^3)/(6*sqrt(2))

Volume of Tetrahedron given Height Formula

LaTeX Go

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

Volume of Tetrahedron given Height calculator uses Volume of Tetrahedron = ((sqrt(3/2)*Height of Tetrahedron)^3)/(6*sqrt(2)) to calculate the Volume of Tetrahedron, The Volume of Tetrahedron given Height formula is defined as the total quantity of three dimensional space enclosed by the surface of the Tetrahedron, and calculated using the height of the Tetrahedron. Volume of Tetrahedron is denoted by V symbol.

How to calculate Volume of Tetrahedron given Height using this online calculator? To use this online calculator for Volume of Tetrahedron given Height, enter Height of Tetrahedron (h) and hit the calculate button. Here is how the Volume of Tetrahedron given Height calculation can be explained with given input values -> 110.8513 = ((sqrt(3/2)*8)^3)/(6*sqrt(2)).

FAQ

What is Volume of Tetrahedron given Height?

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

How to calculate Volume of Tetrahedron given Height?

The Volume of Tetrahedron given Height formula is defined as the total quantity of three dimensional space enclosed by the surface of the Tetrahedron, and calculated using the height of the Tetrahedron is calculated using Volume of Tetrahedron = ((sqrt(3/2)*Height of Tetrahedron)^3)/(6*sqrt(2)). To calculate Volume of Tetrahedron given Height, you need Height of Tetrahedron (h). With our tool, you need to enter the respective value for Height 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 Volume of Tetrahedron?

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

Volume of Tetrahedron = (Edge Length of Tetrahedron^3)/(6*sqrt(2))
Volume of Tetrahedron = sqrt(2)/12*(Total Surface Area of Tetrahedron/sqrt(3))^(3/2)
Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2))

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