Ridge Length of Great Stellated Dodecahedron given Volume Calculator

✖Volume of Great Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron.ⓘ Volume of Great Stellated Dodecahedron [V]

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✖Ridge Length of Great Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron.ⓘ Ridge Length of Great Stellated Dodecahedron given Volume [l_Ridge]

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Formula

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Ridge Length of Great Stellated Dodecahedron given Volume

Formula

`"l"_{"Ridge"} = (1+sqrt(5))/2*((4*"V")/(5*(3+sqrt(5))))^(1/3)`

Example

`"16.18439m"=(1+sqrt(5))/2*((4*"6550m³")/(5*(3+sqrt(5))))^(1/3)`

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Ridge Length of Great Stellated Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)
l_Ridge = (1+sqrt(5))/2*((4*V)/(5*(3+sqrt(5))))^(1/3)
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

Ridge Length of Great Stellated Dodecahedron - (Measured in Meter) - Ridge Length of Great Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron.
Volume of Great Stellated Dodecahedron - (Measured in Cubic Meter) - Volume of Great Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Great Stellated Dodecahedron: 6550 Cubic Meter --> 6550 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_Ridge = (1+sqrt(5))/2*((4*V)/(5*(3+sqrt(5))))^(1/3) --> (1+sqrt(5))/2*((4*6550)/(5*(3+sqrt(5))))^(1/3)

Evaluating ... ...

l_Ridge = 16.1843890800045

STEP 3: Convert Result to Output's Unit

16.1843890800045 Meter --> No Conversion Required

FINAL ANSWER

16.1843890800045 ≈ 16.18439 Meter <-- Ridge Length of Great Stellated Dodecahedron

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Great Stellated Dodecahedron » Length of Great Stellated Dodecahedron » Ridge Length of Great Stellated Dodecahedron » Ridge Length of Great Stellated Dodecahedron given Volume

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< 7 Ridge Length of Great Stellated Dodecahedron Calculators

Ridge Length of Great Stellated Dodecahedron given Total Surface Area

Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))

Ridge Length of Great Stellated Dodecahedron given Surface to Volume Ratio

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

Ridge Length of Great Stellated Dodecahedron given Pyramidal Height

Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))

Ridge Length of Great Stellated Dodecahedron given Circumradius

Go Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*(4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5)))

Ridge Length of Great Stellated Dodecahedron given Volume

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

Ridge Length of Great Stellated Dodecahedron given Pentagram Chord

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

Ridge Length of Great Stellated Dodecahedron

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

Ridge Length of Great Stellated Dodecahedron given Volume Formula

Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3)
l_Ridge = (1+sqrt(5))/2*((4*V)/(5*(3+sqrt(5))))^(1/3)

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 Ridge Length of Great Stellated Dodecahedron given Volume?

Ridge Length of Great Stellated Dodecahedron given Volume calculator uses Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3) to calculate the Ridge Length of Great Stellated Dodecahedron, Ridge Length of Great Stellated Dodecahedron given Volume formula is defined as the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron, calculated using its volume. Ridge Length of Great Stellated Dodecahedron is denoted by l_Ridge symbol.

How to calculate Ridge Length of Great Stellated Dodecahedron given Volume using this online calculator? To use this online calculator for Ridge Length of Great Stellated Dodecahedron given Volume, enter Volume of Great Stellated Dodecahedron (V) and hit the calculate button. Here is how the Ridge Length of Great Stellated Dodecahedron given Volume calculation can be explained with given input values -> 16.18439 = (1+sqrt(5))/2*((4*6550)/(5*(3+sqrt(5))))^(1/3).

FAQ

What is Ridge Length of Great Stellated Dodecahedron given Volume?

Ridge Length of Great Stellated Dodecahedron given Volume formula is defined as the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron, calculated using its volume and is represented as l_Ridge = (1+sqrt(5))/2*((4*V)/(5*(3+sqrt(5))))^(1/3) or Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3). Volume of Great Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron.

How to calculate Ridge Length of Great Stellated Dodecahedron given Volume?

Ridge Length of Great Stellated Dodecahedron given Volume formula is defined as the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron, calculated using its volume is calculated using Ridge Length of Great Stellated Dodecahedron = (1+sqrt(5))/2*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3). To calculate Ridge Length of Great Stellated Dodecahedron given Volume, you need Volume of Great Stellated Dodecahedron (V). With our tool, you need to enter the respective value for Volume 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 Ridge Length of Great Stellated Dodecahedron?

In this formula, Ridge Length of Great Stellated Dodecahedron uses Volume of Great Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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