Surface to Volume Ratio of Great Stellated Dodecahedron given Volume Calculator

✖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 [V]

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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 Volume [AV]

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Surface to Volume Ratio of Great Stellated Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
AV = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*((5*(3+sqrt(5)))/(4*V))^(1/3)
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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Volume of Great Stellated Dodecahedron: 6550 Cubic Meter --> 6550 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AV = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*((5*(3+sqrt(5)))/(4*V))^(1/3) --> (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*((5*(3+sqrt(5)))/(4*6550))^(1/3)

Evaluating ... ...

AV = 0.705165832279824

STEP 3: Convert Result to Output's Unit

0.705165832279824 1 per Meter --> No Conversion Required

FINAL ANSWER

0.705165832279824 ≈ 0.705166 1 per Meter <-- SA:V of Great Stellated Dodecahedron

(Calculation completed in 00.006 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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< 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 Volume 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.

What is Great Stellated Dodecahedron?

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {5⁄2,3}. It is one of four nonconvex regular polyhedra.

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Volume calculator uses 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) to calculate the SA:V of Great Stellated Dodecahedron, Surface to Volume Ratio of Great Stellated Dodecahedron given Volume 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 volume. SA:V of Great Stellated Dodecahedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Great Stellated Dodecahedron given Volume using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Stellated Dodecahedron given Volume, enter Volume of Great Stellated Dodecahedron (V) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Stellated Dodecahedron given Volume calculation can be explained with given input values -> 0.705166 = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*((5*(3+sqrt(5)))/(4*6550))^(1/3).

FAQ

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Volume 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 volume and is represented as AV = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*((5*(3+sqrt(5)))/(4*V))^(1/3) or 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). Volume of Great Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron.

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Volume 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 volume is calculated using 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). To calculate Surface to Volume Ratio of Great Stellated Dodecahedron given Volume, you need Volume of Great Stellated Dodecahedron (V). With our tool, you need to enter the respective value for Volume 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 Volume 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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