Edge Length of Truncated Dodecahedron given Midsphere Radius Calculator

✖Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Truncated Dodecahedron [r_m]

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✖Edge Length of Truncated Dodecahedron is the length of any edge of the Truncated Dodecahedron.ⓘ Edge Length of Truncated Dodecahedron given Midsphere Radius [l_e]

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Formula

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Edge Length of Truncated Dodecahedron given Midsphere Radius

Formula

`"l"_{"e"} = (4*"r"_{"m"})/(5+(3*sqrt(5)))`

Example

`"9.907583m"=(4*"29m")/(5+(3*sqrt(5)))`

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Edge Length of Truncated Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Truncated Dodecahedron = (4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5)))
l_e = (4*r_m)/(5+(3*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

Edge Length of Truncated Dodecahedron - (Measured in Meter) - Edge Length of Truncated Dodecahedron is the length of any edge of the Truncated Dodecahedron.
Midsphere Radius of Truncated Dodecahedron - (Measured in Meter) - Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Truncated Dodecahedron: 29 Meter --> 29 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (4*r_m)/(5+(3*sqrt(5))) --> (4*29)/(5+(3*sqrt(5)))

Evaluating ... ...

l_e = 9.90758280849634

STEP 3: Convert Result to Output's Unit

9.90758280849634 Meter --> No Conversion Required

FINAL ANSWER

9.90758280849634 ≈ 9.907583 Meter <-- Edge Length of Truncated Dodecahedron

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Walchand College of Engineering (WCE), Sangli

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< 6 Edge Length of Truncated Dodecahedron Calculators

Edge Length of Truncated Dodecahedron given Surface to Volume Ratio

Go Edge Length of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))

Edge Length of Truncated Dodecahedron given Total Surface Area

Go Edge Length of Truncated Dodecahedron = sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))

Edge Length of Truncated Dodecahedron given Circumsphere Radius

Go Edge Length of Truncated Dodecahedron = (4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5))))

Edge Length of Truncated Dodecahedron given Volume

Go Edge Length of Truncated Dodecahedron = ((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)

Edge Length of Truncated Dodecahedron given Midsphere Radius

Go Edge Length of Truncated Dodecahedron = (4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5)))

Edge Length of Truncated Dodecahedron given Dodecahedral Edge Length

Go Edge Length of Truncated Dodecahedron = Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)

Edge Length of Truncated Dodecahedron given Midsphere Radius Formula

Edge Length of Truncated Dodecahedron = (4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5)))
l_e = (4*r_m)/(5+(3*sqrt(5)))

What is a Truncated Dodecahedron?

In geometry, the Truncated Dodecahedron is an Archimedean solid. It has a total of 32 faces - 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Each vertex is identical in such a way that two decagonal faces and one triangular face join at each vertex. This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. The Truncated Dodecahedron has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: hexagonal and pentagonal.

How to Calculate Edge Length of Truncated Dodecahedron given Midsphere Radius?

Edge Length of Truncated Dodecahedron given Midsphere Radius calculator uses Edge Length of Truncated Dodecahedron = (4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))) to calculate the Edge Length of Truncated Dodecahedron, Edge Length of Truncated Dodecahedron given Midsphere Radius formula is defined as the length of any edge of the Truncated Dodecahedron, and calculated using the midsphere radius of the Truncated Dodecahedron. Edge Length of Truncated Dodecahedron is denoted by l_e symbol.

How to calculate Edge Length of Truncated Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Edge Length of Truncated Dodecahedron given Midsphere Radius, enter Midsphere Radius of Truncated Dodecahedron (r_m) and hit the calculate button. Here is how the Edge Length of Truncated Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 9.907583 = (4*29)/(5+(3*sqrt(5))).

FAQ

What is Edge Length of Truncated Dodecahedron given Midsphere Radius?

Edge Length of Truncated Dodecahedron given Midsphere Radius formula is defined as the length of any edge of the Truncated Dodecahedron, and calculated using the midsphere radius of the Truncated Dodecahedron and is represented as l_e = (4*r_m)/(5+(3*sqrt(5))) or Edge Length of Truncated Dodecahedron = (4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))). Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere.

How to calculate Edge Length of Truncated Dodecahedron given Midsphere Radius?

Edge Length of Truncated Dodecahedron given Midsphere Radius formula is defined as the length of any edge of the Truncated Dodecahedron, and calculated using the midsphere radius of the Truncated Dodecahedron is calculated using Edge Length of Truncated Dodecahedron = (4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))). To calculate Edge Length of Truncated Dodecahedron given Midsphere Radius, you need Midsphere Radius of Truncated Dodecahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Truncated 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 Edge Length of Truncated Dodecahedron?

In this formula, Edge Length of Truncated Dodecahedron uses Midsphere Radius of Truncated Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Edge Length of Truncated Dodecahedron = Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
Edge Length of Truncated Dodecahedron = sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))
Edge Length of Truncated Dodecahedron = ((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)
Edge Length of Truncated Dodecahedron = (4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5))))
Edge Length of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))

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