Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio Calculator

✖SA:V of Great Stellated Dodecahedron is the numerical ratio of the total surface area of a Great Stellated Dodecahedron to the volume of the Great Stellated Dodecahedron.ⓘ SA:V of Great Stellated Dodecahedron [AV]

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✖Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron.ⓘ Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio [l_c(Pentagram)]

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Formula

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Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio

Formula

`"l"_{"c(Pentagram)"} = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*"AV")`

Example

`"42.68397m"=(2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*"0.7m⁻¹")`

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Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron)
l_c(Pentagram) = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(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

Pentagram Chord of Great Stellated Dodecahedron - (Measured in Meter) - Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron.
SA:V of Great Stellated Dodecahedron - (Measured in 1 per Meter) - SA:V of Great Stellated Dodecahedron is the numerical ratio of the total surface area of a Great Stellated Dodecahedron to the volume of the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

SA:V of Great Stellated Dodecahedron: 0.7 1 per Meter --> 0.7 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c(Pentagram) = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*AV) --> (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*0.7)

Evaluating ... ...

l_c(Pentagram) = 42.6839705979905

STEP 3: Convert Result to Output's Unit

42.6839705979905 Meter --> No Conversion Required

FINAL ANSWER

42.6839705979905 ≈ 42.68397 Meter <-- Pentagram Chord of Great Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 7 Pentagram Chord of Great Stellated Dodecahedron Calculators

Pentagram Chord of Great Stellated Dodecahedron given Total Surface Area

Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))

Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio

Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron)

Pentagram Chord of Great Stellated Dodecahedron given Pyramidal Height

Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))

Pentagram Chord of Great Stellated Dodecahedron given Circumradius

Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))

Pentagram Chord of Great Stellated Dodecahedron given Volume

Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)

Pentagram Chord of Great Stellated Dodecahedron given Ridge Length

Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))

Pentagram Chord of Great Stellated Dodecahedron

Go Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*Edge Length of Great Stellated Dodecahedron

Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio Formula

What is Great Stellated Dodecahedron?

The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {⁵⁄₂,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.

How to Calculate Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio?

Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio calculator uses Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron) to calculate the Pentagram Chord of Great Stellated Dodecahedron, Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron, calculated using its surface to volume ratio. Pentagram Chord of Great Stellated Dodecahedron is denoted by l_c(Pentagram) symbol.

How to calculate Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio, enter SA:V of Great Stellated Dodecahedron (AV) and hit the calculate button. Here is how the Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 42.68397 = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*0.7).

FAQ

What is Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio?

Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron, calculated using its surface to volume ratio and is represented as l_c(Pentagram) = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*AV) or Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron). SA:V of Great Stellated Dodecahedron is the numerical ratio of the total surface area of a Great Stellated Dodecahedron to the volume of the Great Stellated Dodecahedron.

How to calculate Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio?

Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron, calculated using its surface to volume ratio is calculated using Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron). To calculate Pentagram Chord of Great Stellated Dodecahedron given Surface to Volume Ratio, you need SA:V of Great Stellated Dodecahedron (AV). With our tool, you need to enter the respective value for SA:V of Great Stellated Dodecahedron 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 Pentagram Chord of Great Stellated Dodecahedron?

In this formula, Pentagram Chord of Great Stellated Dodecahedron uses SA:V of Great Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*Edge Length of Great Stellated Dodecahedron
Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))
Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))
Pentagram Chord of Great Stellated Dodecahedron = (2+sqrt(5))*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)

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