Volume of Tetragonal Trapezohedron given Surface to Volume Ratio Calculator

✖SA:V of Tetragonal Trapezohedron is the numerical ratio of the total surface area of the Tetragonal Trapezohedron to the volume of the Tetragonal Trapezohedron.ⓘ SA:V of Tetragonal Trapezohedron [AV]

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

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Volume of Tetragonal Trapezohedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
V = (1/3)*sqrt(4+3*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*AV))^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.
SA:V of Tetragonal Trapezohedron - (Measured in 1 per Meter) - SA:V of Tetragonal Trapezohedron is the numerical ratio of the total surface area of the Tetragonal Trapezohedron to the volume of the Tetragonal Trapezohedron.

STEP 1: Convert Input(s) to Base Unit

SA:V of Tetragonal Trapezohedron: 0.6 1 per Meter --> 0.6 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (1/3)*sqrt(4+3*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*AV))^3) --> (1/3)*sqrt(4+3*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*0.6))^3)

Evaluating ... ...

V = 856.816748360279

STEP 3: Convert Result to Output's Unit

856.816748360279 Cubic Meter --> No Conversion Required

FINAL ANSWER

856.816748360279 ≈ 856.8167 Cubic Meter <-- Volume of Tetragonal Trapezohedron

(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru

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< Volume of Tetragonal Trapezohedron Calculators

Volume of Tetragonal Trapezohedron given Long Edge

LaTeX 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

LaTeX 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

LaTeX 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

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

Volume of Tetragonal Trapezohedron given Surface to Volume Ratio Formula

LaTeX Go

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 Surface to Volume Ratio?

Volume of Tetragonal Trapezohedron given Surface to Volume Ratio calculator uses 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) to calculate the Volume of Tetragonal Trapezohedron, The Volume of Tetragonal Trapezohedron given Surface to Volume Ratio formula is defined as the quantity of three-dimensional space enclosed by the Tetragonal Trapezohedron, calculated using its surface to volume ratio. Volume of Tetragonal Trapezohedron is denoted by V symbol.

How to calculate Volume of Tetragonal Trapezohedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Tetragonal Trapezohedron given Surface to Volume Ratio, enter SA:V of Tetragonal Trapezohedron (AV) and hit the calculate button. Here is how the Volume of Tetragonal Trapezohedron given Surface to Volume Ratio calculation can be explained with given input values -> 856.8167 = (1/3)*sqrt(4+3*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*0.6))^3).

FAQ

What is Volume of Tetragonal Trapezohedron given Surface to Volume Ratio?

The Volume of Tetragonal Trapezohedron given Surface to Volume Ratio formula is defined as the quantity of three-dimensional space enclosed by the Tetragonal Trapezohedron, calculated using its surface to volume ratio and is represented as V = (1/3)*sqrt(4+3*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*AV))^3) or 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). SA:V of Tetragonal Trapezohedron is the numerical ratio of the total surface area of the Tetragonal Trapezohedron to the volume of the Tetragonal Trapezohedron.

How to calculate Volume of Tetragonal Trapezohedron given Surface to Volume Ratio?

The Volume of Tetragonal Trapezohedron given Surface to Volume Ratio formula is defined as the quantity of three-dimensional space enclosed by the Tetragonal Trapezohedron, calculated using its surface to volume ratio is calculated using 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). To calculate Volume of Tetragonal Trapezohedron given Surface to Volume Ratio, you need SA:V of Tetragonal Trapezohedron (AV). With our tool, you need to enter the respective value for SA:V 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 SA:V of Tetragonal Trapezohedron. We can use 3 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)

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