Edge Length of Truncated Icosahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Truncated Icosahedron is the numerical ratio of the total surface area of a Truncated Icosahedron to the volume of the Truncated Icosahedron.ⓘ Surface to Volume Ratio of Truncated Icosahedron [R_A/V]

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✖Edge Length of Truncated Icosahedron is the length of any edge of the Truncated Icosahedron.ⓘ Edge Length of Truncated Icosahedron given Surface to Volume Ratio [l_e]

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Edge Length of Truncated Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Truncated Icosahedron = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5))))
l_e = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(R_A/V*(125+(43*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 Icosahedron - (Measured in Meter) - Edge Length of Truncated Icosahedron is the length of any edge of the Truncated Icosahedron.
Surface to Volume Ratio of Truncated Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Truncated Icosahedron is the numerical ratio of the total surface area of a Truncated Icosahedron to the volume of the Truncated Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Truncated Icosahedron: 0.1 1 per Meter --> 0.1 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(R_A/V*(125+(43*sqrt(5)))) --> (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(0.1*(125+(43*sqrt(5))))

Evaluating ... ...

l_e = 13.1326158694742

STEP 3: Convert Result to Output's Unit

13.1326158694742 Meter --> No Conversion Required

FINAL ANSWER

13.1326158694742 ≈ 13.13262 Meter <-- Edge Length of Truncated Icosahedron

(Calculation completed in 00.008 seconds)

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St Joseph's College (SJC), Bengaluru

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Indian Institute of Information Technology (IIIT), Bhopal

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< Edge Length of Truncated Icosahedron Calculators

Edge Length of Truncated Icosahedron given Total Surface Area

LaTeX Go Edge Length of Truncated Icosahedron = sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))))

Edge Length of Truncated Icosahedron given Circumsphere Radius

LaTeX Go Edge Length of Truncated Icosahedron = (4*Circumsphere Radius of Truncated Icosahedron)/(sqrt(58+(18*sqrt(5))))

Edge Length of Truncated Icosahedron given Volume

LaTeX Go Edge Length of Truncated Icosahedron = ((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(1/3)

Edge Length of Truncated Icosahedron given Icosahedral Edge Length

LaTeX Go Edge Length of Truncated Icosahedron = Icosahedral Edge Length of Truncated Icosahedron/3

Edge Length of Truncated Icosahedron given Surface to Volume Ratio Formula

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What is Truncated Icosahedron and its applications?

In geometry, the Truncated Icosahedron is an Archimedean solid, one of 13 convex isogonal non-prismatic solids whose faces are two or more types of regular polygons. It has a total of 32 faces which include 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces. This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons. Geodesic domes such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 ("buckyball") molecule. It is used in the cell-transitive hyperbolic space-filling tessellation, the bi-truncated order-5 dodecahedral honeycomb.

How to Calculate Edge Length of Truncated Icosahedron given Surface to Volume Ratio?

Edge Length of Truncated Icosahedron given Surface to Volume Ratio calculator uses Edge Length of Truncated Icosahedron = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))) to calculate the Edge Length of Truncated Icosahedron, Edge Length of Truncated Icosahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Truncated Icosahedron, and calculated using the surface to volume ratio of the Truncated Icosahedron. Edge Length of Truncated Icosahedron is denoted by l_e symbol.

How to calculate Edge Length of Truncated Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Edge Length of Truncated Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Truncated Icosahedron (R_A/V) and hit the calculate button. Here is how the Edge Length of Truncated Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 13.13262 = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(0.1*(125+(43*sqrt(5)))).

FAQ

What is Edge Length of Truncated Icosahedron given Surface to Volume Ratio?

Edge Length of Truncated Icosahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Truncated Icosahedron, and calculated using the surface to volume ratio of the Truncated Icosahedron and is represented as l_e = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(R_A/V*(125+(43*sqrt(5)))) or Edge Length of Truncated Icosahedron = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))). Surface to Volume Ratio of Truncated Icosahedron is the numerical ratio of the total surface area of a Truncated Icosahedron to the volume of the Truncated Icosahedron.

How to calculate Edge Length of Truncated Icosahedron given Surface to Volume Ratio?

Edge Length of Truncated Icosahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Truncated Icosahedron, and calculated using the surface to volume ratio of the Truncated Icosahedron is calculated using Edge Length of Truncated Icosahedron = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))). To calculate Edge Length of Truncated Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Truncated Icosahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Truncated Icosahedron 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 Icosahedron?

In this formula, Edge Length of Truncated Icosahedron uses Surface to Volume Ratio of Truncated Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Edge Length of Truncated Icosahedron = Icosahedral Edge Length of Truncated Icosahedron/3
Edge Length of Truncated Icosahedron = sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))))
Edge Length of Truncated Icosahedron = ((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(1/3)

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