Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius Calculator

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

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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 Circumradius [AV]

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Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Circumradius of Great Stellated Dodecahedron - (Measured in Meter) - Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Great Stellated Dodecahedron: 23 Meter --> 23 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AV = (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/r_c --> (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/23

Evaluating ... ...

AV = 0.69530925078337

STEP 3: Convert Result to Output's Unit

0.69530925078337 1 per Meter --> No Conversion Required

FINAL ANSWER

0.69530925078337 ≈ 0.695309 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 Circumradius Formula

LaTeX Go

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

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 Circumradius?

Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius calculator uses SA:V of Great Stellated Dodecahedron = (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/Circumradius of Great Stellated Dodecahedron to calculate the SA:V of Great Stellated Dodecahedron, Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius 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 circumradius. SA:V of Great Stellated Dodecahedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius, enter Circumradius of Great Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 0.695309 = (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/23.

FAQ

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius 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 circumradius and is represented as AV = (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/r_c or SA:V of Great Stellated Dodecahedron = (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/Circumradius of Great Stellated Dodecahedron. Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius 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 circumradius is calculated using SA:V of Great Stellated Dodecahedron = (3*sqrt(3)*sqrt(5+(2*sqrt(5))))/Circumradius of Great Stellated Dodecahedron. To calculate Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius, you need Circumradius of Great Stellated Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumradius 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 Circumradius 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 = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(2+sqrt(5))/Pentagram Chord of Great Stellated Dodecahedron

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