Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius Calculator

✖Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.ⓘ Insphere Radius of Pentakis Dodecahedron [r_i]

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✖Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.ⓘ Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius [R_A/V]

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Surface to Volume Ratio of Pentakis Dodecahedron given Insphere 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((81+(35*sqrt(5)))/218)))/(2*Insphere Radius of Pentakis Dodecahedron))
R_A/V = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3*(sqrt((81+(35*sqrt(5)))/218)))/(2*r_i))
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.
Insphere Radius of Pentakis Dodecahedron - (Measured in Meter) - Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Pentakis Dodecahedron: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3*(sqrt((81+(35*sqrt(5)))/218)))/(2*r_i)) --> (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3*(sqrt((81+(35*sqrt(5)))/218)))/(2*12))

Evaluating ... ...

R_A/V = 0.25

STEP 3: Convert Result to Output's Unit

0.25 1 per Meter --> No Conversion Required

FINAL ANSWER

0.25 1 per Meter <-- Surface to Volume Ratio of Pentakis Dodecahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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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 Insphere Radius Formula

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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 Insphere Radius?

Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius calculator uses Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3*(sqrt((81+(35*sqrt(5)))/218)))/(2*Insphere Radius of Pentakis Dodecahedron)) to calculate the Surface to Volume Ratio of Pentakis Dodecahedron, Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius formula is defined as what part of total volume of Pentakis Dodechedron is the total surface area, calculated using insphere radius of Pentakis Dodecahedron. Surface to Volume Ratio of Pentakis Dodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius, enter Insphere Radius of Pentakis Dodecahedron (r_i) and hit the calculate button. Here is how the Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius calculation can be explained with given input values -> 0.25 = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3*(sqrt((81+(35*sqrt(5)))/218)))/(2*12)).

FAQ

What is Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius?

Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius formula is defined as what part of total volume of Pentakis Dodechedron is the total surface area, calculated using insphere radius of Pentakis Dodecahedron and is represented as R_A/V = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3*(sqrt((81+(35*sqrt(5)))/218)))/(2*r_i)) or Surface to Volume Ratio of Pentakis Dodecahedron = (((76/19)*(sqrt(413+(162*sqrt(5)))))/(23+(11*sqrt(5))))*((3*(sqrt((81+(35*sqrt(5)))/218)))/(2*Insphere Radius of Pentakis Dodecahedron)). Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.

How to calculate Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius?

Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius formula is defined as what part of total volume of Pentakis Dodechedron is the total surface area, calculated using insphere 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((81+(35*sqrt(5)))/218)))/(2*Insphere Radius of Pentakis Dodecahedron)). To calculate Surface to Volume Ratio of Pentakis Dodecahedron given Insphere Radius, you need Insphere Radius of Pentakis Dodecahedron (r_i). With our tool, you need to enter the respective value for Insphere 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 Insphere 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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