Volume of Tetragonal Trapezohedron given Height Calculator

✖Height of Tetragonal Trapezohedron is the distance between the two peak vertices where the long edges of Tetragonal Trapezohedron join.ⓘ Height of Tetragonal Trapezohedron [h]

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✖Volume of Tetragonal Trapezohedron is the amount of three dimensional space covered by Tetragonal Trapezohedron.ⓘ Volume of Tetragonal Trapezohedron given Height [V]

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Formula

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Volume of Tetragonal Trapezohedron given Height

Formula

`"V" = (1/3)*sqrt(4+3*sqrt(2))*(("h"/(sqrt((1/2)*(4+3*sqrt(2)))))^3)`

Example

`"915.0553m³"=(1/3)*sqrt(4+3*sqrt(2))*(("20m"/(sqrt((1/2)*(4+3*sqrt(2)))))^3)`

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Volume of Tetragonal Trapezohedron given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^3)
V = (1/3)*sqrt(4+3*sqrt(2))*((h/(sqrt((1/2)*(4+3*sqrt(2)))))^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

Volume of Tetragonal Trapezohedron - (Measured in Cubic Meter) - Volume of Tetragonal Trapezohedron is the amount of three dimensional space covered by Tetragonal Trapezohedron.
Height of Tetragonal Trapezohedron - (Measured in Meter) - Height of Tetragonal Trapezohedron is the distance between the two peak vertices where the long edges of Tetragonal Trapezohedron join.

STEP 1: Convert Input(s) to Base Unit

Height of Tetragonal Trapezohedron: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (1/3)*sqrt(4+3*sqrt(2))*((h/(sqrt((1/2)*(4+3*sqrt(2)))))^3) --> (1/3)*sqrt(4+3*sqrt(2))*((20/(sqrt((1/2)*(4+3*sqrt(2)))))^3)

Evaluating ... ...

V = 915.055334686986

STEP 3: Convert Result to Output's Unit

915.055334686986 Cubic Meter --> No Conversion Required

FINAL ANSWER

915.055334686986 ≈ 915.0553 Cubic Meter <-- Volume of Tetragonal Trapezohedron

(Calculation completed in 00.020 seconds)

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< 6 Volume of Tetragonal Trapezohedron Calculators

Volume of Tetragonal Trapezohedron given Surface to Volume Ratio

Go Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*SA:V of Tetragonal Trapezohedron))^3)

Volume of Tetragonal Trapezohedron given Total Surface Area

Go Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((sqrt(Total Surface Area of Tetragonal Trapezohedron/(2*sqrt(2+4*sqrt(2)))))^3)

Volume of Tetragonal Trapezohedron given Long Edge

Go Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*(((2*Long Edge of Tetragonal Trapezohedron)/(sqrt(2*(1+sqrt(2)))))^3)

Volume of Tetragonal Trapezohedron given Height

Go Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^3)

Volume of Tetragonal Trapezohedron given Short Edge

Go Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))^3)

Volume of Tetragonal Trapezohedron

Go Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*(Antiprism Edge Length of Tetragonal Trapezohedron^3)

Volume of Tetragonal Trapezohedron given Height Formula

Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^3)
V = (1/3)*sqrt(4+3*sqrt(2))*((h/(sqrt((1/2)*(4+3*sqrt(2)))))^3)

What is a Tetragonal Trapezohedron?

In geometry, a Tetragonal Trapezohedron, or deltohedron, is the second in an infinite series of trapezohedra, which are dual to the antiprisms. It has eight faces, which are congruent kites, and is dual to the square antiprism.

What is a Trapezohedron?

The n-gonal Trapezohedron, antidipyramid, antibipyramid, or deltohedron is the dual polyhedron of an n-gonal antiprism. The 2n faces of the n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its 2n faces are kites (also called deltoids). The n-gon part of the name does not refer to faces here but to two arrangements of vertices around an axis of symmetry. The dual n-gonal antiprism has two actual n-gon faces. An n-gonal trapezohedron can be dissected into two equal n-gonal pyramids and an n-gonal antiprism.

How to Calculate Volume of Tetragonal Trapezohedron given Height?

Volume of Tetragonal Trapezohedron given Height calculator uses Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^3) to calculate the Volume of Tetragonal Trapezohedron, The Volume of Tetragonal Trapezohedron given Height formula is defined as the quantity of three-dimensional space enclosed by the Tetragonal Trapezohedron, calculated using its height. Volume of Tetragonal Trapezohedron is denoted by V symbol.

How to calculate Volume of Tetragonal Trapezohedron given Height using this online calculator? To use this online calculator for Volume of Tetragonal Trapezohedron given Height, enter Height of Tetragonal Trapezohedron (h) and hit the calculate button. Here is how the Volume of Tetragonal Trapezohedron given Height calculation can be explained with given input values -> 915.0553 = (1/3)*sqrt(4+3*sqrt(2))*((20/(sqrt((1/2)*(4+3*sqrt(2)))))^3).

FAQ

What is Volume of Tetragonal Trapezohedron given Height?

The Volume of Tetragonal Trapezohedron given Height formula is defined as the quantity of three-dimensional space enclosed by the Tetragonal Trapezohedron, calculated using its height and is represented as V = (1/3)*sqrt(4+3*sqrt(2))*((h/(sqrt((1/2)*(4+3*sqrt(2)))))^3) or Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^3). Height of Tetragonal Trapezohedron is the distance between the two peak vertices where the long edges of Tetragonal Trapezohedron join.

How to calculate Volume of Tetragonal Trapezohedron given Height?

The Volume of Tetragonal Trapezohedron given Height formula is defined as the quantity of three-dimensional space enclosed by the Tetragonal Trapezohedron, calculated using its height is calculated using Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^3). To calculate Volume of Tetragonal Trapezohedron given Height, you need Height of Tetragonal Trapezohedron (h). With our tool, you need to enter the respective value for Height of Tetragonal Trapezohedron 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 Tetragonal Trapezohedron?

In this formula, Volume of Tetragonal Trapezohedron uses Height of Tetragonal Trapezohedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*(Antiprism Edge Length of Tetragonal Trapezohedron^3)
Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))^3)
Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*(((2*Long Edge of Tetragonal Trapezohedron)/(sqrt(2*(1+sqrt(2)))))^3)
Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*((sqrt(Total Surface Area of Tetragonal Trapezohedron/(2*sqrt(2+4*sqrt(2)))))^3)
Volume of Tetragonal Trapezohedron = (1/3)*sqrt(4+3*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*SA:V of Tetragonal Trapezohedron))^3)

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