Volume of Great Dodecahedron Calculator

✖Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.ⓘ Edge Length of Great Dodecahedron [l_e]

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✖Volume of Great Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron.ⓘ Volume of Great Dodecahedron [V]

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Volume of Great Dodecahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron^3
V = 5/4*(sqrt(5)-1)*l_e^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 Dodecahedron - (Measured in Cubic Meter) - Volume of Great Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron.
Edge Length of Great Dodecahedron - (Measured in Meter) - Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Great Dodecahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/4*(sqrt(5)-1)*l_e^3 --> 5/4*(sqrt(5)-1)*10^3

Evaluating ... ...

V = 1545.08497187474

STEP 3: Convert Result to Output's Unit

1545.08497187474 Cubic Meter --> No Conversion Required

FINAL ANSWER

1545.08497187474 ≈ 1545.085 Cubic Meter <-- Volume of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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Credits

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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< Volume of Great Dodecahedron Calculators

Volume of Great Dodecahedron given Circumsphere Radius

LaTeX Go Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^3

Volume of Great Dodecahedron given Pyramidal Height

LaTeX Go Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^3

Volume of Great Dodecahedron given Ridge Length

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

Volume of Great Dodecahedron

LaTeX Go Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron^3

Volume of Great Dodecahedron Formula

LaTeX Go

Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron^3
V = 5/4*(sqrt(5)-1)*l_e^3

What is Great Dodecahedron?

The Great Dodecahedron is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Volume of Great Dodecahedron?

Volume of Great Dodecahedron calculator uses Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron^3 to calculate the Volume of Great Dodecahedron, Volume of Great Dodecahedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron. Volume of Great Dodecahedron is denoted by V symbol.

How to calculate Volume of Great Dodecahedron using this online calculator? To use this online calculator for Volume of Great Dodecahedron, enter Edge Length of Great Dodecahedron (l_e) and hit the calculate button. Here is how the Volume of Great Dodecahedron calculation can be explained with given input values -> 1545.085 = 5/4*(sqrt(5)-1)*10^3.

FAQ

What is Volume of Great Dodecahedron?

Volume of Great Dodecahedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron and is represented as V = 5/4*(sqrt(5)-1)*l_e^3 or Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron^3. Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.

How to calculate Volume of Great Dodecahedron?

Volume of Great Dodecahedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron is calculated using Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron^3. To calculate Volume of Great Dodecahedron, you need Edge Length of Great Dodecahedron (l_e). With our tool, you need to enter the respective value for Edge Length of Great 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 Dodecahedron?

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

Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^3
Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^3
Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^3

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