Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio Calculator

✖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.ⓘ SA:V of Pentagonal Trapezohedron [AV]

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✖Long Edge of Pentagonal Trapezohedron is the length of the any of the longer edges of the Pentagonal Trapezohedron.ⓘ Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio [l_e(Long)]

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Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

SA:V of Pentagonal Trapezohedron: 0.4 1 per Meter --> 0.4 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Long) = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*AV)) --> ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.4))

Evaluating ... ...

l_e(Long) = 17.6335575687742

STEP 3: Convert Result to Output's Unit

17.6335575687742 Meter --> No Conversion Required

FINAL ANSWER

17.6335575687742 ≈ 17.63356 Meter <-- Long Edge of Pentagonal Trapezohedron

(Calculation completed in 00.007 seconds)

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St Joseph's College (SJC), Bengaluru

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Indian Institute of Information Technology (IIIT), Bhopal

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< Long Edge of Pentagonal Trapezohedron Calculators

Long Edge of Pentagonal Trapezohedron given Total Surface Area

LaTeX Go Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*(sqrt(Total Surface Area of Pentagonal Trapezohedron/((sqrt((25/2)*(5+sqrt(5)))))))

Long Edge of Pentagonal Trapezohedron given Height

LaTeX Go Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))

Long Edge of Pentagonal Trapezohedron given Short Edge

LaTeX Go Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2)))

Long Edge of Pentagonal Trapezohedron

LaTeX Go Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*Antiprism Edge Length of Pentagonal Trapezohedron

Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio Formula

LaTeX Go

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 Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio?

Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio calculator uses Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*SA:V of Pentagonal Trapezohedron)) to calculate the Long Edge of Pentagonal Trapezohedron, The Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio formula is defined as the length of the any of the longer edges of the Pentagonal Trapezohedron, calculated using its surface to volume ratio. Long Edge of Pentagonal Trapezohedron is denoted by l_e(Long) symbol.

How to calculate Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio, enter SA:V of Pentagonal Trapezohedron (AV) and hit the calculate button. Here is how the Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio calculation can be explained with given input values -> 17.63356 = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.4)).

FAQ

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

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

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

The Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio formula is defined as the length of the any of the longer edges of the Pentagonal Trapezohedron, calculated using its surface to volume ratio is calculated using Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*SA:V of Pentagonal Trapezohedron)). To calculate Long Edge of Pentagonal Trapezohedron given Surface to Volume Ratio, you need SA:V of Pentagonal Trapezohedron (AV). With our tool, you need to enter the respective value for SA:V 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 Long Edge of Pentagonal Trapezohedron?

In this formula, Long Edge of Pentagonal Trapezohedron uses SA:V of Pentagonal Trapezohedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*Antiprism Edge Length of Pentagonal Trapezohedron
Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2)))
Long Edge of Pentagonal Trapezohedron = ((sqrt(5)+1)/2)*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))

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