Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length Calculator

✖Dodecahedral Edge Length of Truncated Dodecahedron is the length of any edge of the larger dodecahedron from which the corners are cut to form the Truncated Dodecahedron.ⓘ Dodecahedral Edge Length of Truncated Dodecahedron [l_{e(Dodecahedron)}]

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✖Surface to Volume Ratio of Truncated Dodecahedron is the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron.ⓘ Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length [R_A/V]

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Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)*(99+(47*sqrt(5))))
R_A/V = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(l_{e(Dodecahedron)}/sqrt(5)*(99+(47*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

Surface to Volume Ratio of Truncated Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Truncated Dodecahedron is the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron.
Dodecahedral Edge Length of Truncated Dodecahedron - (Measured in Meter) - Dodecahedral Edge Length of Truncated Dodecahedron is the length of any edge of the larger dodecahedron from which the corners are cut to form the Truncated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Dodecahedral Edge Length of Truncated Dodecahedron: 22 Meter --> 22 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(l_{e(Dodecahedron)}/sqrt(5)*(99+(47*sqrt(5)))) --> (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(22/sqrt(5)*(99+(47*sqrt(5))))

Evaluating ... ...

R_A/V = 0.120704211687463

STEP 3: Convert Result to Output's Unit

0.120704211687463 1 per Meter --> No Conversion Required

FINAL ANSWER

0.120704211687463 ≈ 0.120704 1 per Meter <-- Surface to Volume Ratio of Truncated Dodecahedron

(Calculation completed in 00.020 seconds)

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< Surface to Volume Ratio of Truncated Dodecahedron Calculators

Surface to Volume Ratio of Truncated Dodecahedron given Total Surface Area

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

Surface to Volume Ratio of Truncated Dodecahedron given Volume

LaTeX Go Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)*(99+(47*sqrt(5))))

Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length

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

Surface to Volume Ratio of Truncated Dodecahedron

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

Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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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 Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length?

Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length calculator uses Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)*(99+(47*sqrt(5)))) to calculate the Surface to Volume Ratio of Truncated Dodecahedron, Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length formula is defined as the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron, and calculated using the dodecahedral edge length of the Truncated Dodecahedron. Surface to Volume Ratio of Truncated Dodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length using this online calculator? To use this online calculator for Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length, enter Dodecahedral Edge Length of Truncated Dodecahedron (l_{e(Dodecahedron)}) and hit the calculate button. Here is how the Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length calculation can be explained with given input values -> 0.120704 = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(22/sqrt(5)*(99+(47*sqrt(5)))).

FAQ

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

Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length formula is defined as the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron, and calculated using the dodecahedral edge length of the Truncated Dodecahedron and is represented as R_A/V = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(l_{e(Dodecahedron)}/sqrt(5)*(99+(47*sqrt(5)))) or Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)*(99+(47*sqrt(5)))). Dodecahedral Edge Length of Truncated Dodecahedron is the length of any edge of the larger dodecahedron from which the corners are cut to form the Truncated Dodecahedron.

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

Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length formula is defined as the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron, and calculated using the dodecahedral edge length of the Truncated Dodecahedron is calculated using Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)*(99+(47*sqrt(5)))). To calculate Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length, you need Dodecahedral Edge Length of Truncated Dodecahedron (l_{e(Dodecahedron)}). With our tool, you need to enter the respective value for Dodecahedral Edge Length 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 Surface to Volume Ratio of Truncated Dodecahedron?

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

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

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