Volume of Pentagonal Hexecontahedron given Long Edge Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Pentagonal Hexecontahedron = 5*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
V = 5*((31*le(Long))/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
This formula uses 1 Constants, 1 Functions, 2 Variables
Constants Used
[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811
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 Pentagonal Hexecontahedron - (Measured in Cubic Meter) - Volume of Pentagonal Hexecontahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron.
Long Edge of Pentagonal Hexecontahedron - (Measured in Meter) - Long Edge of Pentagonal Hexecontahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron.
STEP 1: Convert Input(s) to Base Unit
Long Edge of Pentagonal Hexecontahedron: 6 Meter --> 6 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = 5*((31*le(Long))/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)) --> 5*((31*6)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
Evaluating ... ...
V = 16035.0063951357
STEP 3: Convert Result to Output's Unit
16035.0063951357 Cubic Meter --> No Conversion Required
FINAL ANSWER
16035.0063951357 16035.01 Cubic Meter <-- Volume of Pentagonal Hexecontahedron
(Calculation completed in 00.004 seconds)

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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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Volume of Pentagonal Hexecontahedron Calculators

Volume of Pentagonal Hexecontahedron given Long Edge
​ LaTeX ​ Go Volume of Pentagonal Hexecontahedron = 5*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
Volume of Pentagonal Hexecontahedron given Total Surface Area
​ LaTeX ​ Go Volume of Pentagonal Hexecontahedron = 5*((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
Volume of Pentagonal Hexecontahedron given Snub Dodecahedron Edge
​ LaTeX ​ Go Volume of Pentagonal Hexecontahedron = 5*(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
Volume of Pentagonal Hexecontahedron
​ LaTeX ​ Go Volume of Pentagonal Hexecontahedron = 5*Short Edge of Pentagonal Hexecontahedron^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Volume of Pentagonal Hexecontahedron given Long Edge Formula

​LaTeX ​Go
Volume of Pentagonal Hexecontahedron = 5*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
V = 5*((31*le(Long))/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

What is Pentagonal Hexecontahedron?

In geometry, a Pentagonal Hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. It has 60 faces, 150 edges, 92 vertices. It is the Catalan solid with the most vertices. Among the Catalan and Archimedean solids, it has the second largest number of vertices, after the truncated icosidodecahedron, which has 120 vertices.

How to Calculate Volume of Pentagonal Hexecontahedron given Long Edge?

Volume of Pentagonal Hexecontahedron given Long Edge calculator uses Volume of Pentagonal Hexecontahedron = 5*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)) to calculate the Volume of Pentagonal Hexecontahedron, Volume of Pentagonal Hexecontahedron given Long Edge formula is defined as the quantity of three-dimensional space enclosed by the entire surface of the Pentagonal Hexecontahedron, calculated using long edge of Pentagonal Hexecontahedron. Volume of Pentagonal Hexecontahedron is denoted by V symbol.

How to calculate Volume of Pentagonal Hexecontahedron given Long Edge using this online calculator? To use this online calculator for Volume of Pentagonal Hexecontahedron given Long Edge, enter Long Edge of Pentagonal Hexecontahedron (le(Long)) and hit the calculate button. Here is how the Volume of Pentagonal Hexecontahedron given Long Edge calculation can be explained with given input values -> 16035.01 = 5*((31*6)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)).

FAQ

What is Volume of Pentagonal Hexecontahedron given Long Edge?
Volume of Pentagonal Hexecontahedron given Long Edge formula is defined as the quantity of three-dimensional space enclosed by the entire surface of the Pentagonal Hexecontahedron, calculated using long edge of Pentagonal Hexecontahedron and is represented as V = 5*((31*le(Long))/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)) or Volume of Pentagonal Hexecontahedron = 5*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)). Long Edge of Pentagonal Hexecontahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron.
How to calculate Volume of Pentagonal Hexecontahedron given Long Edge?
Volume of Pentagonal Hexecontahedron given Long Edge formula is defined as the quantity of three-dimensional space enclosed by the entire surface of the Pentagonal Hexecontahedron, calculated using long edge of Pentagonal Hexecontahedron is calculated using Volume of Pentagonal Hexecontahedron = 5*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)). To calculate Volume of Pentagonal Hexecontahedron given Long Edge, you need Long Edge of Pentagonal Hexecontahedron (le(Long)). With our tool, you need to enter the respective value for Long Edge of Pentagonal Hexecontahedron 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 Pentagonal Hexecontahedron?
In this formula, Volume of Pentagonal Hexecontahedron uses Long Edge of Pentagonal Hexecontahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Volume of Pentagonal Hexecontahedron = 5*Short Edge of Pentagonal Hexecontahedron^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
  • Volume of Pentagonal Hexecontahedron = 5*(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
  • Volume of Pentagonal Hexecontahedron = 5*((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
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