Surface to Volume Ratio of Great Dodecahedron Calculator

✖Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.ⓘ Edge Length of Great Dodecahedron [l_e]

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✖Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.ⓘ Surface to Volume Ratio of Great Dodecahedron [R_A/V]

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Formula

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Surface to Volume Ratio of Great Dodecahedron

Formula

`"R"_{"A/V"} = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*"l"_{"e"})`

Example

`"0.705342m⁻¹"=(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*"10m")`

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Surface to Volume Ratio of Great Dodecahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron)
R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*l_e)
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

Surface to Volume Ratio of Great Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.
Edge Length of Great Dodecahedron - (Measured in Meter) - Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Great Dodecahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*l_e) --> (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*10)

Evaluating ... ...

R_A/V = 0.705342302750968

STEP 3: Convert Result to Output's Unit

0.705342302750968 1 per Meter --> No Conversion Required

FINAL ANSWER

0.705342302750968 ≈ 0.705342 1 per Meter <-- Surface to Volume Ratio of Great Dodecahedron

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< 6 Surface to Volume Ratio of Great Dodecahedron Calculators

Surface to Volume Ratio of Great Dodecahedron given Total Surface Area

Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt((15*sqrt(5-(2*sqrt(5))))/Total Surface Area of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius

Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt(10+(2*sqrt(5)))/(4*Circumsphere Radius of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height

Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*Pyramidal Height of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron given Volume

Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*((5*(sqrt(5)-1))/(4*Volume of Great Dodecahedron))^(1/3)

Surface to Volume Ratio of Great Dodecahedron

Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron given Ridge Length

Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4)*1/(2*Ridge Length of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron Formula

Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron)
R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*l_e)

What is Great Dodecahedron?

The Great Dodecahedron is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Surface to Volume Ratio of Great Dodecahedron?

Surface to Volume Ratio of Great Dodecahedron calculator uses Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron) to calculate the Surface to Volume Ratio of Great Dodecahedron, Surface to Volume Ratio of Great Dodecahedron formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron. Surface to Volume Ratio of Great Dodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Great Dodecahedron using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Dodecahedron, enter Edge Length of Great Dodecahedron (l_e) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Dodecahedron calculation can be explained with given input values -> 0.705342 = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*10).

FAQ

What is Surface to Volume Ratio of Great Dodecahedron?

Surface to Volume Ratio of Great Dodecahedron formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron and is represented as R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*l_e) or Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron). Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.

How to calculate Surface to Volume Ratio of Great Dodecahedron?

Surface to Volume Ratio of Great Dodecahedron formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron is calculated using Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron). To calculate Surface to Volume Ratio of Great Dodecahedron, you need Edge Length of Great Dodecahedron (l_e). With our tool, you need to enter the respective value for Edge Length of Great 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 Surface to Volume Ratio of Great Dodecahedron?

In this formula, Surface to Volume Ratio of Great Dodecahedron uses Edge Length of Great Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4)*1/(2*Ridge Length of Great Dodecahedron)
Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt(10+(2*sqrt(5)))/(4*Circumsphere Radius of Great Dodecahedron)
Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*Pyramidal Height of Great Dodecahedron)
Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt((15*sqrt(5-(2*sqrt(5))))/Total Surface Area of Great Dodecahedron)
Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*((5*(sqrt(5)-1))/(4*Volume of Great Dodecahedron))^(1/3)

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