Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge Calculator

✖Short Edge of Tetragonal Trapezohedron is the length of any of the shorter edges of the Tetragonal Trapezohedron.ⓘ Short Edge of Tetragonal Trapezohedron [l_e(Short)]

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✖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.ⓘ Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge [AV]

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Formula

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Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge

Formula

`"AV" = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*("l"_{"e(Short)"}/(sqrt(sqrt(2)-1))))`

Example

`"0.620303m⁻¹"=(2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*("6m"/(sqrt(sqrt(2)-1))))`

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Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

SA:V of Tetragonal Trapezohedron = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1))))
AV = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(l_e(Short)/(sqrt(sqrt(2)-1))))
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

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.
Short Edge of Tetragonal Trapezohedron - (Measured in Meter) - Short Edge of Tetragonal Trapezohedron is the length of any of the shorter edges of the Tetragonal Trapezohedron.

STEP 1: Convert Input(s) to Base Unit

Short Edge of Tetragonal Trapezohedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AV = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(l_e(Short)/(sqrt(sqrt(2)-1)))) --> (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(6/(sqrt(sqrt(2)-1))))

Evaluating ... ...

AV = 0.620303402255893

STEP 3: Convert Result to Output's Unit

0.620303402255893 1 per Meter --> No Conversion Required

FINAL ANSWER

0.620303402255893 ≈ 0.620303 1 per Meter <-- SA:V of Tetragonal Trapezohedron

(Calculation completed in 00.020 seconds)

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< 6 Surface to Volume Ratio of Tetragonal Trapezohedron Calculators

Surface to Volume Ratio of Tetragonal Trapezohedron given Total Surface Area

Go SA:V of Tetragonal Trapezohedron = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(sqrt(Total Surface Area of Tetragonal Trapezohedron/(2*sqrt(2+4*sqrt(2))))))

Surface to Volume Ratio of Tetragonal Trapezohedron given Volume

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

Surface to Volume Ratio of Tetragonal Trapezohedron given Long Edge

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

Surface to Volume Ratio of Tetragonal Trapezohedron given Height

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

Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge

Go SA:V of Tetragonal Trapezohedron = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1))))

Surface to Volume Ratio of Tetragonal Trapezohedron

Go SA:V of Tetragonal Trapezohedron = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*Antiprism Edge Length of Tetragonal Trapezohedron)

Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge Formula

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 Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge?

Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge calculator uses SA:V of Tetragonal Trapezohedron = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))) to calculate the SA:V of Tetragonal Trapezohedron, Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge formula is defined as the numerical ratio of the total surface area of a Tetragonal Trapezohedron to the volume of the Tetragonal Trapezohedron, calculated using its short edge. SA:V of Tetragonal Trapezohedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge using this online calculator? To use this online calculator for Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge, enter Short Edge of Tetragonal Trapezohedron (l_e(Short)) and hit the calculate button. Here is how the Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge calculation can be explained with given input values -> 0.620303 = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(6/(sqrt(sqrt(2)-1)))).

FAQ

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

Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge formula is defined as the numerical ratio of the total surface area of a Tetragonal Trapezohedron to the volume of the Tetragonal Trapezohedron, calculated using its short edge and is represented as AV = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(l_e(Short)/(sqrt(sqrt(2)-1)))) or SA:V of Tetragonal Trapezohedron = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))). Short Edge of Tetragonal Trapezohedron is the length of any of the shorter edges of the Tetragonal Trapezohedron.

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

Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge formula is defined as the numerical ratio of the total surface area of a Tetragonal Trapezohedron to the volume of the Tetragonal Trapezohedron, calculated using its short edge is calculated using SA:V of Tetragonal Trapezohedron = (2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*(Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))). To calculate Surface to Volume Ratio of Tetragonal Trapezohedron given Short Edge, you need Short Edge of Tetragonal Trapezohedron (l_e(Short)). With our tool, you need to enter the respective value for Short Edge 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 SA:V of Tetragonal Trapezohedron?

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

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

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