Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(SA:V of Deltoidal Hexecontahedron*(370+(164*sqrt(5)))/25)
ri = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(AV*(370+(164*sqrt(5)))/25)
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
Insphere Radius of Deltoidal Hexecontahedron - (Measured in Meter) - Insphere Radius of Deltoidal Hexecontahedron is the radius of the sphere that is contained by the Deltoidal Hexecontahedron in such a way that all the faces just touch the sphere.
SA:V of Deltoidal Hexecontahedron - (Measured in 1 per Meter) - SA:V of Deltoidal Hexecontahedron is what part of or fraction of total volume of Deltoidal Hexecontahedron is the total surface area.
STEP 1: Convert Input(s) to Base Unit
SA:V of Deltoidal Hexecontahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(AV*(370+(164*sqrt(5)))/25) --> 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(0.2*(370+(164*sqrt(5)))/25)
Evaluating ... ...
ri = 2.76319454874843
STEP 3: Convert Result to Output's Unit
2.76319454874843 Meter --> No Conversion Required
FINAL ANSWER
2.76319454874843 2.763195 Meter <-- Insphere Radius of Deltoidal Hexecontahedron
(Calculation completed in 00.004 seconds)

Credits

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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8 Insphere Radius of Deltoidal Hexecontahedron Calculators

Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio
Go Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(SA:V of Deltoidal Hexecontahedron*(370+(164*sqrt(5)))/25)
Insphere Radius of Deltoidal Hexecontahedron given Total Surface Area
Go Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*sqrt((11*Total Surface Area of Deltoidal Hexecontahedron)/(9*sqrt(10*(157+(31*sqrt(5))))))
Insphere Radius of Deltoidal Hexecontahedron given NonSymmetry Diagonal
Go Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(11*NonSymmetry Diagonal of Deltoidal Hexecontahedron)/(sqrt((470+(156*sqrt(5)))/5))
Insphere Radius of Deltoidal Hexecontahedron given Volume
Go Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*((11*Volume of Deltoidal Hexecontahedron)/(45*sqrt((370+(164*sqrt(5)))/25)))^(1/3)
Insphere Radius of Deltoidal Hexecontahedron given Symmetry Diagonal
Go Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*Symmetry Diagonal of Deltoidal Hexecontahedron/(3*sqrt((5-sqrt(5))/20))
Insphere Radius of Deltoidal Hexecontahedron given Midsphere Radius
Go Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(20*Midsphere Radius of Deltoidal Hexecontahedron)/(3*(5+(3*sqrt(5))))
Insphere Radius of Deltoidal Hexecontahedron given Short Edge
Go Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(22*Short Edge of Deltoidal Hexecontahedron)/(3*(7-sqrt(5)))
Insphere Radius of Deltoidal Hexecontahedron
Go Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*Long Edge of Deltoidal Hexecontahedron

Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio Formula

Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(SA:V of Deltoidal Hexecontahedron*(370+(164*sqrt(5)))/25)
ri = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(AV*(370+(164*sqrt(5)))/25)

What is Deltoidal Hexecontahedron?

A Deltoidal Hexecontahedron is a polyhedron with deltoid (kite) faces, those have two angles with 86.97°, one angle with 118.3° and one with 67.8°. It has twenty vertices with three edges, thirty vertices with four edges and twelve vertices with five edges. In total, it has 60 faces, 120 edges, 62 vertices.

How to Calculate Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio?

Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio calculator uses Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(SA:V of Deltoidal Hexecontahedron*(370+(164*sqrt(5)))/25) to calculate the Insphere Radius of Deltoidal Hexecontahedron, Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Deltoidal Hexecontahedron in such a way that all the faces just touch the sphere, calculated using surface to volume ratio of Deltoidal Hexecontahedron. Insphere Radius of Deltoidal Hexecontahedron is denoted by ri symbol.

How to calculate Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio, enter SA:V of Deltoidal Hexecontahedron (AV) and hit the calculate button. Here is how the Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio calculation can be explained with given input values -> 2.763195 = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(0.2*(370+(164*sqrt(5)))/25).

FAQ

What is Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio?
Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Deltoidal Hexecontahedron in such a way that all the faces just touch the sphere, calculated using surface to volume ratio of Deltoidal Hexecontahedron and is represented as ri = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(AV*(370+(164*sqrt(5)))/25) or Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(SA:V of Deltoidal Hexecontahedron*(370+(164*sqrt(5)))/25). SA:V of Deltoidal Hexecontahedron is what part of or fraction of total volume of Deltoidal Hexecontahedron is the total surface area.
How to calculate Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio?
Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Deltoidal Hexecontahedron in such a way that all the faces just touch the sphere, calculated using surface to volume ratio of Deltoidal Hexecontahedron is calculated using Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(SA:V of Deltoidal Hexecontahedron*(370+(164*sqrt(5)))/25). To calculate Insphere Radius of Deltoidal Hexecontahedron given Surface to Volume Ratio, you need SA:V of Deltoidal Hexecontahedron (AV). With our tool, you need to enter the respective value for SA:V of Deltoidal 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 Insphere Radius of Deltoidal Hexecontahedron?
In this formula, Insphere Radius of Deltoidal Hexecontahedron uses SA:V of Deltoidal Hexecontahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*Long Edge of Deltoidal Hexecontahedron
  • Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(22*Short Edge of Deltoidal Hexecontahedron)/(3*(7-sqrt(5)))
  • Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*Symmetry Diagonal of Deltoidal Hexecontahedron/(3*sqrt((5-sqrt(5))/20))
  • Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(11*NonSymmetry Diagonal of Deltoidal Hexecontahedron)/(sqrt((470+(156*sqrt(5)))/5))
  • Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*sqrt((11*Total Surface Area of Deltoidal Hexecontahedron)/(9*sqrt(10*(157+(31*sqrt(5))))))
  • Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*((11*Volume of Deltoidal Hexecontahedron)/(45*sqrt((370+(164*sqrt(5)))/25)))^(1/3)
  • Insphere Radius of Deltoidal Hexecontahedron = 3/2*sqrt((135+(59*sqrt(5)))/205)*(20*Midsphere Radius of Deltoidal Hexecontahedron)/(3*(5+(3*sqrt(5))))
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