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))))/rc
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))))/rc --> (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 00.020 seconds)

Credits

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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7 Surface to Volume Ratio of Great Stellated Dodecahedron Calculators

Surface to Volume Ratio of Great Stellated Dodecahedron given Total Surface Area
Go SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*sqrt((15*sqrt(5+(2*sqrt(5))))/Total Surface Area of Great Stellated Dodecahedron)
Surface to Volume Ratio of Great Stellated Dodecahedron given Volume
Go SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*((5*(3+sqrt(5)))/(4*Volume of Great Stellated Dodecahedron))^(1/3)
Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length
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
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
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 Pyramidal Height
Go SA:V of Great Stellated Dodecahedron = (2*sqrt(3)*sqrt(5+(2*sqrt(5))))/Pyramidal Height of Great Stellated Dodecahedron
Surface to Volume Ratio of Great Stellated Dodecahedron given Circumradius
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

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))))/rc

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 (rc) 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))))/rc 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 (rc). 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 6 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
  • SA:V of Great Stellated Dodecahedron = (2*sqrt(3)*sqrt(5+(2*sqrt(5))))/Pyramidal Height of Great Stellated Dodecahedron
  • SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*sqrt((15*sqrt(5+(2*sqrt(5))))/Total Surface Area of Great Stellated Dodecahedron)
  • SA:V of Great Stellated Dodecahedron = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*((5*(3+sqrt(5)))/(4*Volume of Great Stellated Dodecahedron))^(1/3)
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