Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge Calculator

✖Long Edge of Pentagonal Trapezohedron is the length of the any of the longer edges of the Pentagonal Trapezohedron.ⓘ Long Edge of Pentagonal Trapezohedron [l_e(Long)]

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✖SA:V of Pentagonal Trapezohedron is the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron.ⓘ Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge [AV]

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Formula

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Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge

Formula

`"AV" = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*("l"_{"e(Long)"}/(((sqrt(5)+1)/2))))`

Example

`"0.440839m⁻¹"=((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*("16m"/(((sqrt(5)+1)/2))))`

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Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2))))
AV = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(l_e(Long)/(((sqrt(5)+1)/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

SA:V of Pentagonal Trapezohedron - (Measured in 1 per Meter) - SA:V of Pentagonal Trapezohedron is the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron.
Long Edge of Pentagonal Trapezohedron - (Measured in Meter) - Long Edge of Pentagonal Trapezohedron is the length of the any of the longer edges of the Pentagonal Trapezohedron.

STEP 1: Convert Input(s) to Base Unit

Long Edge of Pentagonal Trapezohedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AV = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(l_e(Long)/(((sqrt(5)+1)/2)))) --> ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(16/(((sqrt(5)+1)/2))))

Evaluating ... ...

AV = 0.440838939219355

STEP 3: Convert Result to Output's Unit

0.440838939219355 1 per Meter --> No Conversion Required

FINAL ANSWER

0.440838939219355 ≈ 0.440839 1 per Meter <-- SA:V of Pentagonal Trapezohedron

(Calculation completed in 00.004 seconds)

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< 6 Surface to Volume Ratio of Pentagonal Trapezohedron Calculators

Surface to Volume Ratio of Pentagonal Trapezohedron given Total Surface Area

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(sqrt(Total Surface Area of Pentagonal Trapezohedron/((sqrt((25/2)*(5+sqrt(5))))))))

Surface to Volume Ratio of Pentagonal Trapezohedron given Height

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5))))))

Surface to Volume Ratio of Pentagonal Trapezohedron given Volume

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(((12*Volume of Pentagonal Trapezohedron)/(5*(3+sqrt(5))))^(1/3)))

Surface to Volume Ratio of Pentagonal Trapezohedron given Short Edge

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2))))

Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2))))

Surface to Volume Ratio of Pentagonal Trapezohedron

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*Antiprism Edge Length of Pentagonal Trapezohedron)

Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge Formula

What is a Pentagonal Trapezohedron?

In geometry, a Pentagonal Trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites. It can be decomposed into two pentagonal pyramids and a pentagonal antiprism in the middle. It can also be decomposed into two pentagonal pyramids and a dodecahedron in the middle.

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 Pentagonal Trapezohedron given Long Edge?

Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge calculator uses SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))) to calculate the SA:V of Pentagonal Trapezohedron, Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge formula is defined as the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron, calculated using its long edge. SA:V of Pentagonal Trapezohedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge using this online calculator? To use this online calculator for Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge, enter Long Edge of Pentagonal Trapezohedron (l_e(Long)) and hit the calculate button. Here is how the Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge calculation can be explained with given input values -> 0.440839 = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(16/(((sqrt(5)+1)/2)))).

FAQ

What is Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge?

Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge formula is defined as the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron, calculated using its long edge and is represented as AV = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(l_e(Long)/(((sqrt(5)+1)/2)))) or SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))). Long Edge of Pentagonal Trapezohedron is the length of the any of the longer edges of the Pentagonal Trapezohedron.

How to calculate Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge?

Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge formula is defined as the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron, calculated using its long edge is calculated using SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))). To calculate Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge, you need Long Edge of Pentagonal Trapezohedron (l_e(Long)). With our tool, you need to enter the respective value for Long Edge of Pentagonal 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 Pentagonal Trapezohedron?

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

SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*Antiprism Edge Length of Pentagonal Trapezohedron)
SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2))))
SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5))))))
SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(sqrt(Total Surface Area of Pentagonal Trapezohedron/((sqrt((25/2)*(5+sqrt(5))))))))
SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(((12*Volume of Pentagonal Trapezohedron)/(5*(3+sqrt(5))))^(1/3)))

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