Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))
lLeg = (3/38)*(9+sqrt(5))*((76/19)/(RA/V))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))
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
Leg Length of Pentakis Dodecahedron - (Measured in Meter) - Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron.
Surface to Volume Ratio of Pentakis Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Pentakis Dodecahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
lLeg = (3/38)*(9+sqrt(5))*((76/19)/(RA/V))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) --> (3/38)*(9+sqrt(5))*((76/19)/(0.2))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))
Evaluating ... ...
lLeg = 10.3782388901644
STEP 3: Convert Result to Output's Unit
10.3782388901644 Meter --> No Conversion Required
FINAL ANSWER
10.3782388901644 10.37824 Meter <-- Leg Length of Pentakis Dodecahedron
(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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6 Leg Length of Pentakis Dodecahedron Calculators

Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio
Go Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))
Leg Length of Pentakis Dodecahedron given Total Surface Area
Go Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))
Leg Length of Pentakis Dodecahedron given Insphere Radius
Go Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))
Leg Length of Pentakis Dodecahedron given Volume
Go Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))
Leg Length of Pentakis Dodecahedron given Midsphere Radius
Go Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))
Leg Length of Pentakis Dodecahedron
Go Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*Base Length of Pentakis Dodecahedron

Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio Formula

Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))
lLeg = (3/38)*(9+sqrt(5))*((76/19)/(RA/V))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))

What is Pentakis Dodecahedron?

A Pentakis Dodecahedron is a polyhedron with isosceles triangle faces. Five of these are attached as a pyramid on each face of a dodecahedron.
It has 60 faces, 90 edges, 32 vertices.

How to Calculate Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio?

Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio calculator uses Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) to calculate the Leg Length of Pentakis Dodecahedron, Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron. Leg Length of Pentakis Dodecahedron is denoted by lLeg symbol.

How to calculate Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Pentakis Dodecahedron (RA/V) and hit the calculate button. Here is how the Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 10.37824 = (3/38)*(9+sqrt(5))*((76/19)/(0.2))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))).

FAQ

What is Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio?
Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron and is represented as lLeg = (3/38)*(9+sqrt(5))*((76/19)/(RA/V))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) or Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))). Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.
How to calculate Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio?
Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron is calculated using Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))). To calculate Leg Length of Pentakis Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Pentakis Dodecahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Pentakis 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 Leg Length of Pentakis Dodecahedron?
In this formula, Leg Length of Pentakis Dodecahedron uses Surface to Volume Ratio of Pentakis Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*Base Length of Pentakis Dodecahedron
  • Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))
  • Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))
  • Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))
  • Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))
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