Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*Midsphere Radius of Pentakis Dodecahedron))
RA/V = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*rm))
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
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.
Midsphere Radius of Pentakis Dodecahedron - (Measured in Meter) - Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Pentakis Dodecahedron: 13 Meter --> 13 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RA/V = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*rm)) --> (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*13))
Evaluating ... ...
RA/V = 0.235615347086188
STEP 3: Convert Result to Output's Unit
0.235615347086188 1 per Meter --> No Conversion Required
FINAL ANSWER
0.235615347086188 0.235615 1 per Meter <-- Surface to Volume Ratio of Pentakis Dodecahedron
(Calculation completed in 00.020 seconds)

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Walchand College of Engineering (WCE), Sangli
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Indian Institute of Information Technology (IIIT), Bhopal
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Surface to Volume Ratio of Pentakis Dodecahedron Calculators

Surface to Volume Ratio of Pentakis Dodecahedron given Total Surface Area
​ LaTeX ​ Go Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*(((15*(sqrt(413+(162*sqrt(5)))))/(19*Total Surface Area of Pentakis Dodecahedron))^(0.5))
Surface to Volume Ratio of Pentakis Dodecahedron given Volume
​ LaTeX ​ Go Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*(((15*(23+(11*sqrt(5))))/(76*Volume of Pentakis Dodecahedron))^(1/3))
Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius
​ LaTeX ​ Go Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*Midsphere Radius of Pentakis Dodecahedron))
Surface to Volume Ratio of Pentakis Dodecahedron given Leg Length
​ LaTeX ​ Go Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*(3*((9+sqrt(5)))/(38*Leg Length of Pentakis Dodecahedron))

Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius Formula

​LaTeX ​Go
Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*Midsphere Radius of Pentakis Dodecahedron))
RA/V = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*rm))

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 Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius?

Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius calculator uses Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*Midsphere Radius of Pentakis Dodecahedron)) to calculate the Surface to Volume Ratio of Pentakis Dodecahedron, Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius formula is defined as what part of total volume of Pentakis Dodechedron is the total surface area, calculated using midsphere radius of Pentakis Dodecahedron. Surface to Volume Ratio of Pentakis Dodecahedron is denoted by RA/V symbol.

How to calculate Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius, enter Midsphere Radius of Pentakis Dodecahedron (rm) and hit the calculate button. Here is how the Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 0.235615 = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*13)).

FAQ

What is Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius?
Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius formula is defined as what part of total volume of Pentakis Dodechedron is the total surface area, calculated using midsphere radius of Pentakis Dodecahedron and is represented as RA/V = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*rm)) or Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*Midsphere Radius of Pentakis Dodecahedron)). Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.
How to calculate Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius?
Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius formula is defined as what part of total volume of Pentakis Dodechedron is the total surface area, calculated using midsphere radius of Pentakis Dodecahedron is calculated using Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3+sqrt(5))/(4*Midsphere Radius of Pentakis Dodecahedron)). To calculate Surface to Volume Ratio of Pentakis Dodecahedron given Midsphere Radius, you need Midsphere Radius of Pentakis Dodecahedron (rm). With our tool, you need to enter the respective value for Midsphere Radius 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 Surface to Volume Ratio of Pentakis Dodecahedron?
In this formula, Surface to Volume Ratio of Pentakis Dodecahedron uses Midsphere Radius of Pentakis Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*(3*((9+sqrt(5)))/(38*Leg Length of Pentakis Dodecahedron))
  • Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*(((15*(sqrt(413+(162*sqrt(5)))))/(19*Total Surface Area of Pentakis Dodecahedron))^(0.5))
  • Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*(((15*(23+(11*sqrt(5))))/(76*Volume of Pentakis Dodecahedron))^(1/3))
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