Insphere Radius of Pentagonal Icositetrahedron given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))
ri = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(V^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))
This formula uses 1 Constants, 1 Functions, 2 Variables
Constants Used
[Tribonacci_C] - Tribonacci constant Value Taken As 1.839286755214161
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
Insphere Radius of Pentagonal Icositetrahedron - (Measured in Meter) - Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.
Volume of Pentagonal Icositetrahedron - (Measured in Cubic Meter) - Volume of Pentagonal Icositetrahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Icositetrahedron.
STEP 1: Convert Input(s) to Base Unit
Volume of Pentagonal Icositetrahedron: 7500 Cubic Meter --> 7500 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(V^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6)) --> (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(7500^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))
Evaluating ... ...
ri = 11.6038111998941
STEP 3: Convert Result to Output's Unit
11.6038111998941 Meter --> No Conversion Required
FINAL ANSWER
11.6038111998941 11.60381 Meter <-- Insphere Radius of Pentagonal Icositetrahedron
(Calculation completed in 00.019 seconds)

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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7 Insphere Radius of Pentagonal Icositetrahedron Calculators

Insphere Radius of Pentagonal Icositetrahedron given Surface to Volume Ratio
Go Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*((3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(SA:V of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))))
Insphere Radius of Pentagonal Icositetrahedron given Total Surface Area
Go Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(sqrt(Total Surface Area of Pentagonal Icositetrahedron/3)*(((4*[Tribonacci_C])-3)/(22*((5*[Tribonacci_C])-1)))^(1/4))
Insphere Radius of Pentagonal Icositetrahedron given Volume
Go Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))
Insphere Radius of Pentagonal Icositetrahedron given Short Edge
Go Insphere Radius of Pentagonal Icositetrahedron = 1/2*sqrt(([Tribonacci_C]+1)/((2-[Tribonacci_C])*(3-[Tribonacci_C])))*Short Edge of Pentagonal Icositetrahedron
Insphere Radius of Pentagonal Icositetrahedron given Long Edge
Go Insphere Radius of Pentagonal Icositetrahedron = Long Edge of Pentagonal Icositetrahedron/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1))
Insphere Radius of Pentagonal Icositetrahedron
Go Insphere Radius of Pentagonal Icositetrahedron = Snub Cube Edge of Pentagonal Icositetrahedron/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])))
Insphere Radius of Pentagonal Icositetrahedron given Midsphere Radius
Go Insphere Radius of Pentagonal Icositetrahedron = Midsphere Radius of Pentagonal Icositetrahedron/sqrt(3-[Tribonacci_C])

Insphere Radius of Pentagonal Icositetrahedron given Volume Formula

Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))
ri = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(V^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))

What is Pentagonal Icositetrahedron?

The Pentagonal Icositetrahedron can be constructed from a snub cube. Its faces are axial-symmetric pentagons with the top angle acos(2-t)=80.7517°. Of this polyhedron, there are two forms that are mirror images of each other, but otherwise identical. It has 24 faces, 60 edges, and 38 vertices.

How to Calculate Insphere Radius of Pentagonal Icositetrahedron given Volume?

Insphere Radius of Pentagonal Icositetrahedron given Volume calculator uses Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6)) to calculate the Insphere Radius of Pentagonal Icositetrahedron, Insphere Radius of Pentagonal Icositetrahedron given Volume formula is defined as the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere, calculated using the volume of Pentagonal Icositetrahedron. Insphere Radius of Pentagonal Icositetrahedron is denoted by ri symbol.

How to calculate Insphere Radius of Pentagonal Icositetrahedron given Volume using this online calculator? To use this online calculator for Insphere Radius of Pentagonal Icositetrahedron given Volume, enter Volume of Pentagonal Icositetrahedron (V) and hit the calculate button. Here is how the Insphere Radius of Pentagonal Icositetrahedron given Volume calculation can be explained with given input values -> 11.60381 = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(7500^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6)).

FAQ

What is Insphere Radius of Pentagonal Icositetrahedron given Volume?
Insphere Radius of Pentagonal Icositetrahedron given Volume formula is defined as the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere, calculated using the volume of Pentagonal Icositetrahedron and is represented as ri = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(V^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6)) or Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6)). Volume of Pentagonal Icositetrahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Icositetrahedron.
How to calculate Insphere Radius of Pentagonal Icositetrahedron given Volume?
Insphere Radius of Pentagonal Icositetrahedron given Volume formula is defined as the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere, calculated using the volume of Pentagonal Icositetrahedron is calculated using Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6)). To calculate Insphere Radius of Pentagonal Icositetrahedron given Volume, you need Volume of Pentagonal Icositetrahedron (V). With our tool, you need to enter the respective value for Volume of Pentagonal Icositetrahedron 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 Insphere Radius of Pentagonal Icositetrahedron?
In this formula, Insphere Radius of Pentagonal Icositetrahedron uses Volume of Pentagonal Icositetrahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Insphere Radius of Pentagonal Icositetrahedron = Long Edge of Pentagonal Icositetrahedron/sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])*([Tribonacci_C]+1))
  • Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*(sqrt(Total Surface Area of Pentagonal Icositetrahedron/3)*(((4*[Tribonacci_C])-3)/(22*((5*[Tribonacci_C])-1)))^(1/4))
  • Insphere Radius of Pentagonal Icositetrahedron = (1/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))))*((3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(SA:V of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))))
  • Insphere Radius of Pentagonal Icositetrahedron = Snub Cube Edge of Pentagonal Icositetrahedron/(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C])))
  • Insphere Radius of Pentagonal Icositetrahedron = 1/2*sqrt(([Tribonacci_C]+1)/((2-[Tribonacci_C])*(3-[Tribonacci_C])))*Short Edge of Pentagonal Icositetrahedron
  • Insphere Radius of Pentagonal Icositetrahedron = Midsphere Radius of Pentagonal Icositetrahedron/sqrt(3-[Tribonacci_C])
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