Volume of Great Stellated Dodecahedron given Surface to Volume Ratio Calculator

✖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.ⓘ SA:V of Great Stellated Dodecahedron [AV]

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✖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 given Surface to Volume Ratio [V]

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Volume of Great Stellated Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^3
V = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*AV))^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

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.
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.

STEP 1: Convert Input(s) to Base Unit

SA:V of Great Stellated Dodecahedron: 0.7 1 per Meter --> 0.7 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*AV))^3 --> 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*0.7))^3

Evaluating ... ...

V = 6696.08508032218

STEP 3: Convert Result to Output's Unit

6696.08508032218 Cubic Meter --> No Conversion Required

FINAL ANSWER

6696.08508032218 ≈ 6696.085 Cubic Meter <-- Volume of Great Stellated Dodecahedron

(Calculation completed in 00.020 seconds)

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< Volume of Great Stellated Dodecahedron Calculators

Volume of Great Stellated Dodecahedron given Circumradius

LaTeX Go Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3

Volume of Great Stellated Dodecahedron given Ridge Length

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

Volume of Great Stellated Dodecahedron given Pentagram Chord

LaTeX Go Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^3

Volume of Great Stellated Dodecahedron

LaTeX Go Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*Edge Length of Great Stellated Dodecahedron^3

Volume of Great Stellated Dodecahedron given Surface to Volume Ratio Formula

LaTeX Go

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 Volume of Great Stellated Dodecahedron given Surface to Volume Ratio?

Volume of Great Stellated Dodecahedron given Surface to Volume Ratio calculator uses Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^3 to calculate the Volume of Great Stellated Dodecahedron, Volume of Great Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron, calculated using its surface to volume ratio. Volume of Great Stellated Dodecahedron is denoted by V symbol.

How to calculate Volume of Great Stellated Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Great Stellated Dodecahedron given Surface to Volume Ratio, enter SA:V of Great Stellated Dodecahedron (AV) and hit the calculate button. Here is how the Volume of Great Stellated Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 6696.085 = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*0.7))^3.

FAQ

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

Volume of Great Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron, calculated using its surface to volume ratio and is represented as V = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*AV))^3 or Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^3. 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.

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

Volume of Great Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron, calculated using its surface to volume ratio is calculated using Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^3. To calculate Volume of Great Stellated Dodecahedron given Surface to Volume Ratio, you need SA:V of Great Stellated Dodecahedron (AV). With our tool, you need to enter the respective value for SA:V 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 Volume of Great Stellated Dodecahedron?

In this formula, Volume of Great Stellated Dodecahedron uses SA:V of Great Stellated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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