Volume of Pentagonal Hexecontahedron given Midsphere Radius Calculator

✖Midsphere Radius of Pentagonal Hexecontahedron is the radius of the sphere for which all the edges of the Pentagonal Hexecontahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Pentagonal Hexecontahedron [r_m]

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✖Volume of Pentagonal Hexecontahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron.ⓘ Volume of Pentagonal Hexecontahedron given Midsphere Radius [V]

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Formula

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Volume of Pentagonal Hexecontahedron given Midsphere Radius

Formula

`"V" = 5*("r"_{"m"}/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))`

Example

`"13756.23m³"=5*("15m"/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))`

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Volume of Pentagonal Hexecontahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Pentagonal Hexecontahedron = 5*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
V = 5*(r_m/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
This formula uses 1 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 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.
Midsphere Radius of Pentagonal Hexecontahedron - (Measured in Meter) - Midsphere Radius of Pentagonal Hexecontahedron is the radius of the sphere for which all the edges of the Pentagonal Hexecontahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Pentagonal Hexecontahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5*(r_m/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)) --> 5*(15/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Evaluating ... ...

V = 13756.233949899

STEP 3: Convert Result to Output's Unit

13756.233949899 Cubic Meter --> No Conversion Required

FINAL ANSWER

13756.233949899 ≈ 13756.23 Cubic Meter <-- Volume of Pentagonal Hexecontahedron

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » CatalanSolids » Pentagonal Hexecontahedron » Volume of Pentagonal Hexecontahedron » Volume of Pentagonal Hexecontahedron given Midsphere Radius

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 6 Volume of Pentagonal Hexecontahedron Calculators

Volume of Pentagonal Hexecontahedron given Long Edge

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

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 Insphere Radius

Go Volume of Pentagonal Hexecontahedron = 5*((Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*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 Midsphere Radius

Go Volume of Pentagonal Hexecontahedron = 5*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*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 Snub Dodecahedron Edge

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

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 Midsphere Radius Formula

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 Midsphere Radius?

Volume of Pentagonal Hexecontahedron given Midsphere Radius calculator uses Volume of Pentagonal Hexecontahedron = 5*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*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 Midsphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron, calculated using midsphere radius of Pentagonal Hexecontahedron. Volume of Pentagonal Hexecontahedron is denoted by V symbol.

How to calculate Volume of Pentagonal Hexecontahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Pentagonal Hexecontahedron given Midsphere Radius, enter Midsphere Radius of Pentagonal Hexecontahedron (r_m) and hit the calculate button. Here is how the Volume of Pentagonal Hexecontahedron given Midsphere Radius calculation can be explained with given input values -> 13756.23 = 5*(15/sqrt((1+0.4715756)/(2*(1-2*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 Midsphere Radius?

Volume of Pentagonal Hexecontahedron given Midsphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron, calculated using midsphere radius of Pentagonal Hexecontahedron and is represented as V = 5*(r_m/sqrt((1+0.4715756)/(2*(1-2*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*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)). Midsphere Radius of Pentagonal Hexecontahedron is the radius of the sphere for which all the edges of the Pentagonal Hexecontahedron become a tangent line on that sphere.

How to calculate Volume of Pentagonal Hexecontahedron given Midsphere Radius?

Volume of Pentagonal Hexecontahedron given Midsphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron, calculated using midsphere radius of Pentagonal Hexecontahedron is calculated using Volume of Pentagonal Hexecontahedron = 5*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*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 Midsphere Radius, you need Midsphere Radius of Pentagonal Hexecontahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius 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 Midsphere Radius of Pentagonal Hexecontahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

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 = 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))
Volume of Pentagonal Hexecontahedron = 5*((Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

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