Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Calculator

✖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 [R_A/V]

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✖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.ⓘ Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio [r_m]

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Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))
r_m = ((3+sqrt(5))/4)*((76/19)/(R_A/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

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.
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

r_m = ((3+sqrt(5))/4)*((76/19)/(R_A/V))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) --> ((3+sqrt(5))/4)*((76/19)/(0.2))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))

Evaluating ... ...

r_m = 15.3149975606022

STEP 3: Convert Result to Output's Unit

15.3149975606022 Meter --> No Conversion Required

FINAL ANSWER

15.3149975606022 ≈ 15.315 Meter <-- Midsphere Radius of Pentakis Dodecahedron

(Calculation completed in 00.020 seconds)

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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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< Midsphere Radius of Pentakis Dodecahedron Calculators

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio

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

Midsphere Radius of Pentakis Dodecahedron given Total Surface Area

LaTeX Go Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))

Midsphere Radius of Pentakis Dodecahedron given Leg Length

LaTeX Go Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))

Midsphere Radius of Pentakis Dodecahedron

LaTeX Go Midsphere Radius of Pentakis Dodecahedron = (Base Length of Pentakis Dodecahedron/4)*(3+sqrt(5))

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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 Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio?

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio calculator uses Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) to calculate the Midsphere Radius of Pentakis Dodecahedron, Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere, calculated using the surface to volume ratio of the Pentakis Dodecahedron. Midsphere Radius of Pentakis Dodecahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Pentakis Dodecahedron (R_A/V) and hit the calculate button. Here is how the Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 15.315 = ((3+sqrt(5))/4)*((76/19)/(0.2))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))).

FAQ

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

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere, calculated using the surface to volume ratio of the Pentakis Dodecahedron and is represented as r_m = ((3+sqrt(5))/4)*((76/19)/(R_A/V))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) or Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((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 Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio?

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere, calculated using the surface to volume ratio of the Pentakis Dodecahedron is calculated using Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))). To calculate Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Pentakis Dodecahedron (R_A/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 Midsphere Radius of Pentakis Dodecahedron?

In this formula, Midsphere Radius of Pentakis Dodecahedron uses Surface to Volume Ratio of Pentakis Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Midsphere Radius of Pentakis Dodecahedron = (Base Length of Pentakis Dodecahedron/4)*(3+sqrt(5))
Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))
Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))

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