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

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

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✖SA:V of Small Stellated Dodecahedron is the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron.ⓘ Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord [AV]

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Formula

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Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord

Formula

`"AV" = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/"l"_{"c(Pentagram)"})`

Example

`"0.27173m⁻¹"=((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/"42m")`

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

STEP 0: Pre-Calculation Summary

Formula Used

SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/Pentagram Chord of Small Stellated Dodecahedron)
AV = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+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 Small Stellated Dodecahedron - (Measured in 1 per Meter) - SA:V of Small Stellated Dodecahedron is the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron.
Pentagram Chord of Small Stellated Dodecahedron - (Measured in Meter) - Pentagram Chord of Small Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Small Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagram Chord of Small 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)*(7+3*sqrt(5))))*((2+sqrt(5))/l_c(Pentagram)) --> ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/42)

Evaluating ... ...

AV = 0.271730433227187

STEP 3: Convert Result to Output's Unit

0.271730433227187 1 per Meter --> No Conversion Required

FINAL ANSWER

0.271730433227187 ≈ 0.27173 1 per Meter <-- SA:V of Small Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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< 7 Surface to Volume Ratio of Small Stellated Dodecahedron Calculators

Surface to Volume Ratio of Small Stellated Dodecahedron given Total Surface Area

Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*(sqrt((15*(sqrt(5+2*sqrt(5))))/Total Surface Area of Small Stellated Dodecahedron))

Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height

Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(25+10*sqrt(5)))/(5*Pyramidal Height of Small Stellated Dodecahedron))

Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius

Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*Circumradius of Small Stellated Dodecahedron))

Surface to Volume Ratio of Small Stellated Dodecahedron given Volume

Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*(((5*(7+3*sqrt(5)))/(4*Volume of Small Stellated Dodecahedron))^(1/3))

Surface to Volume Ratio of Small Stellated Dodecahedron given Ridge Length

Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((1+sqrt(5))/(2*Ridge Length of Small Stellated Dodecahedron))

Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord

Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/Pentagram Chord of Small Stellated Dodecahedron)

Surface to Volume Ratio of Small Stellated Dodecahedron

Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*(1/Edge Length of Small Stellated Dodecahedron)

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

What is Small Stellated Dodecahedron?

The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.

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

Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord calculator uses SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/Pentagram Chord of Small Stellated Dodecahedron) to calculate the SA:V of Small Stellated Dodecahedron, Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord formula is defined as the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron, calculated using its pentagram chord. SA:V of Small Stellated Dodecahedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord using this online calculator? To use this online calculator for Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord, enter Pentagram Chord of Small Stellated Dodecahedron (l_c(Pentagram)) and hit the calculate button. Here is how the Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord calculation can be explained with given input values -> 0.27173 = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/42).

FAQ

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

Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord formula is defined as the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron, calculated using its pentagram chord and is represented as AV = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/l_c(Pentagram)) or SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/Pentagram Chord of Small Stellated Dodecahedron). Pentagram Chord of Small Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Small Stellated Dodecahedron.

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

Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord formula is defined as the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron, calculated using its pentagram chord is calculated using SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/Pentagram Chord of Small Stellated Dodecahedron). To calculate Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord, you need Pentagram Chord of Small Stellated Dodecahedron (l_c(Pentagram)). With our tool, you need to enter the respective value for Pentagram Chord of Small 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 Small Stellated Dodecahedron?

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

SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*(1/Edge Length of Small Stellated Dodecahedron)
SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((1+sqrt(5))/(2*Ridge Length of Small Stellated Dodecahedron))
SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(25+10*sqrt(5)))/(5*Pyramidal Height of Small Stellated Dodecahedron))
SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*(sqrt((15*(sqrt(5+2*sqrt(5))))/Total Surface Area of Small Stellated Dodecahedron))
SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*(((5*(7+3*sqrt(5)))/(4*Volume of Small Stellated Dodecahedron))^(1/3))
SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*Circumradius of Small Stellated Dodecahedron))

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