Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length Calculator

✖Ridge Length of Great Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron.ⓘ Ridge Length of Great Stellated Dodecahedron [l_Ridge]

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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 Ridge Length [AV]

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Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length

Formula

`"AV" = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(1+sqrt(5))/(2*"l"_{"Ridge"})`

Example

`"0.713292m⁻¹"=(15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(1+sqrt(5))/(2*"16m")`

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Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length 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)))*(1+sqrt(5))/(2*Ridge Length of Great Stellated Dodecahedron)
AV = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(1+sqrt(5))/(2*l_Ridge)
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.
Ridge Length of Great Stellated Dodecahedron - (Measured in Meter) - Ridge Length of Great Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Ridge Length of Great Stellated Dodecahedron: 16 Meter --> 16 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)))*(1+sqrt(5))/(2*l_Ridge) --> (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(1+sqrt(5))/(2*16)

Evaluating ... ...

AV = 0.713292387221365

STEP 3: Convert Result to Output's Unit

0.713292387221365 1 per Meter --> No Conversion Required

FINAL ANSWER

0.713292387221365 ≈ 0.713292 1 per Meter <-- SA:V of Great Stellated Dodecahedron

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Great Stellated Dodecahedron » Surface to Volume Ratio of Great Stellated Dodecahedron » Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length

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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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< 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 Ridge Length Formula

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 Ridge Length?

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

How to calculate Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length, enter Ridge Length of Great Stellated Dodecahedron (l_Ridge) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length calculation can be explained with given input values -> 0.713292 = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(1+sqrt(5))/(2*16).

FAQ

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

Surface to Volume Ratio of Great Stellated Dodecahedron given Ridge Length 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 ridge length and is represented as AV = (15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5)))*(1+sqrt(5))/(2*l_Ridge) or 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). Ridge Length of Great Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron.

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

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