Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.ⓘ Circumsphere Radius of Great Dodecahedron [r_c]

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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 given Circumsphere Radius [R_A/V]

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Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius 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))*sqrt(10+(2*sqrt(5)))/(4*Circumsphere Radius of Great Dodecahedron)
R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt(10+(2*sqrt(5)))/(4*r_c)
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.
Circumsphere Radius of Great Dodecahedron - (Measured in Meter) - Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Great Dodecahedron: 9 Meter --> 9 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))*sqrt(10+(2*sqrt(5)))/(4*r_c) --> (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt(10+(2*sqrt(5)))/(4*9)

Evaluating ... ...

R_A/V = 0.74535599249993

STEP 3: Convert Result to Output's Unit

0.74535599249993 1 per Meter --> No Conversion Required

FINAL ANSWER

0.74535599249993 ≈ 0.745356 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

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Indian Institute of Information Technology (IIIT), Bhopal

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< Surface to Volume Ratio of Great Dodecahedron Calculators

Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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 given Circumsphere Radius Formula

LaTeX Go

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 given Circumsphere Radius?

Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius calculator uses 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) to calculate the Surface to Volume Ratio of Great Dodecahedron, Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron, calculated using its circumsphere radius. Surface to Volume Ratio of Great Dodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Great Dodecahedron (r_c) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 0.745356 = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt(10+(2*sqrt(5)))/(4*9).

FAQ

What is Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius?

Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron, calculated using its circumsphere radius and is represented as R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt(10+(2*sqrt(5)))/(4*r_c) or 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). Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.

How to calculate Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius?

Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron, calculated using its circumsphere radius is calculated using 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). To calculate Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius, you need Circumsphere Radius of Great Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Circumsphere Radius of Great Dodecahedron. We can use 3 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*(sqrt(5)-1)*Edge Length of Great Dodecahedron)
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(3)*(3-sqrt(5)))/(6*Pyramidal Height of Great Dodecahedron)

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