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

✖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 [l_c(Pentagram)]

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✖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.ⓘ Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord [AV]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

STEP 1: Convert Input(s) to Base Unit

Pentagram Chord of Great Stellated Dodecahedron: 42 Meter --> 42 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AV = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(2+sqrt(5))/l_c(Pentagram) --> (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(2+sqrt(5))/42

Evaluating ... ...

AV = 0.711399509966509

STEP 3: Convert Result to Output's Unit

0.711399509966509 1 per Meter --> No Conversion Required

FINAL ANSWER

0.711399509966509 ≈ 0.7114 1 per Meter <-- SA:V 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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< Surface to Volume Ratio of Great Stellated Dodecahedron Calculators

Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length

LaTeX Go SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(1+sqrt(5))/(2*Ridge Length of Great Stellated Dodecahedron)

Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord

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

Surface to Volume Ratio of Great Stellated Dodecahedron

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius

LaTeX Go SA:V of Great Stellated Dodecahedron = (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/Circumradius of Great Stellated Dodecahedron

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

LaTeX Go

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord calculator uses SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(2+sqrt(5))/Pentagram Chord of Great Stellated Dodecahedron to calculate the SA:V of Great Stellated Dodecahedron, Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord formula is defined as the numerical ratio of the total surface area of a Great Stellated Dodecahedron to the volume of the Great Stellated Dodecahedron, calculated using its pentagram chord. SA:V of Great Stellated Dodecahedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord, enter Pentagram Chord of Great Stellated Dodecahedron (l_c(Pentagram)) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord calculation can be explained with given input values -> 0.7114 = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(2+sqrt(5))/42.

FAQ

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

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

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord formula is defined as the numerical ratio of the total surface area of a Great Stellated Dodecahedron to the volume of the Great Stellated Dodecahedron, calculated using its pentagram chord is calculated using SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(2+sqrt(5))/Pentagram Chord of Great Stellated Dodecahedron. To calculate Surface to Volume Ratio of Great Stellated Dodecahedron given Pentagram Chord, you need Pentagram Chord of Great Stellated Dodecahedron (l_c(Pentagram)). With our tool, you need to enter the respective value for Pentagram Chord 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 SA:V of Great Stellated Dodecahedron?

In this formula, SA:V of Great Stellated Dodecahedron uses Pentagram Chord of Great Stellated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*Edge Length of Great Stellated Dodecahedron)
SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(1+sqrt(5))/(2*Ridge Length of Great Stellated Dodecahedron)
SA:V of Great Stellated Dodecahedron = (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/Circumradius of Great Stellated Dodecahedron

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