Midsphere Radius of Pentakis Dodecahedron given Leg Length Calculator

✖Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron.ⓘ Leg Length of Pentakis Dodecahedron [l_Leg]

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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 Leg Length [r_m]

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Midsphere Radius of Pentakis Dodecahedron given Leg Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))
r_m = ((3+sqrt(5))/4)*((38*l_Leg)/(3*(9+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.
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.

STEP 1: Convert Input(s) to Base Unit

Leg Length of Pentakis Dodecahedron: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = ((3+sqrt(5))/4)*((38*l_Leg)/(3*(9+sqrt(5)))) --> ((3+sqrt(5))/4)*((38*9)/(3*(9+sqrt(5))))

Evaluating ... ...

r_m = 13.2811529493745

STEP 3: Convert Result to Output's Unit

13.2811529493745 Meter --> No Conversion Required

FINAL ANSWER

13.2811529493745 ≈ 13.28115 Meter <-- Midsphere Radius of Pentakis Dodecahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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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 Leg Length Formula

LaTeX Go

Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))
r_m = ((3+sqrt(5))/4)*((38*l_Leg)/(3*(9+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 Midsphere Radius of Pentakis Dodecahedron given Leg Length?

Midsphere Radius of Pentakis Dodecahedron given Leg Length calculator uses Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5)))) to calculate the Midsphere Radius of Pentakis Dodecahedron, Midsphere Radius of Pentakis Dodecahedron given Leg Length 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 leg length of the Pentakis Dodecahedron. Midsphere Radius of Pentakis Dodecahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Pentakis Dodecahedron given Leg Length using this online calculator? To use this online calculator for Midsphere Radius of Pentakis Dodecahedron given Leg Length, enter Leg Length of Pentakis Dodecahedron (l_Leg) and hit the calculate button. Here is how the Midsphere Radius of Pentakis Dodecahedron given Leg Length calculation can be explained with given input values -> 13.28115 = ((3+sqrt(5))/4)*((38*9)/(3*(9+sqrt(5)))).

FAQ

What is Midsphere Radius of Pentakis Dodecahedron given Leg Length?

Midsphere Radius of Pentakis Dodecahedron given Leg Length 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 leg length of the Pentakis Dodecahedron and is represented as r_m = ((3+sqrt(5))/4)*((38*l_Leg)/(3*(9+sqrt(5)))) or Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5)))). Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron.

How to calculate Midsphere Radius of Pentakis Dodecahedron given Leg Length?

Midsphere Radius of Pentakis Dodecahedron given Leg Length 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 leg length of the Pentakis Dodecahedron is calculated using Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5)))). To calculate Midsphere Radius of Pentakis Dodecahedron given Leg Length, you need Leg Length of Pentakis Dodecahedron (l_Leg). With our tool, you need to enter the respective value for Leg Length 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 Leg Length 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)*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*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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