Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio Calculator

✖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 [R_A/V]

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✖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 given Surface to Volume Ratio [r_m]

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Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))
r_m = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(R_A/V*(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

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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(R_A/V*(99+(47*sqrt(5)))) --> (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(0.1*(99+(47*sqrt(5))))

Evaluating ... ...

r_m = 34.7608501661344

STEP 3: Convert Result to Output's Unit

34.7608501661344 Meter --> No Conversion Required

FINAL ANSWER

34.7608501661344 ≈ 34.76085 Meter <-- Midsphere Radius of Truncated Dodecahedron

(Calculation completed in 00.020 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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< Midsphere Radius of Truncated Dodecahedron Calculators

Midsphere Radius of Truncated Dodecahedron given Total Surface Area

LaTeX Go Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))

Midsphere Radius of Truncated Dodecahedron given Volume

LaTeX Go Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)

Midsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length

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

Midsphere Radius of Truncated Dodecahedron

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

Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio Formula

LaTeX Go

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 Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio?

Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio calculator uses Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))) to calculate the Midsphere Radius of Truncated Dodecahedron, Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere, and calculated using the surface to volume ratio of the Truncated Dodecahedron. Midsphere Radius of Truncated Dodecahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Truncated Dodecahedron (R_A/V) and hit the calculate button. Here is how the Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 34.76085 = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(0.1*(99+(47*sqrt(5)))).

FAQ

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

Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere, and calculated using the surface to volume ratio of the Truncated Dodecahedron and is represented as r_m = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(R_A/V*(99+(47*sqrt(5)))) or Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))). 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.

How to calculate Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio?

Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere, and calculated using the surface to volume ratio of the Truncated Dodecahedron is calculated using Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))). To calculate Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Truncated Dodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Midsphere Radius of Truncated Dodecahedron?

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

Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))

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