Midsphere Radius of Rhombic Triacontahedron given Insphere Radius Calculator

✖Insphere Radius of Rhombic Triacontahedron is the radius of the sphere that is contained by the Rhombic Triacontahedron in such a way that all the faces are just touching the sphere.ⓘ Insphere Radius of Rhombic Triacontahedron [r_i]

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✖Midsphere Radius of Rhombic Triacontahedron is the radius of the sphere for which all the edges of the Rhombic Triacontahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Rhombic Triacontahedron given Insphere Radius [r_m]

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Midsphere Radius of Rhombic Triacontahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Rhombic Triacontahedron = (Insphere Radius of Rhombic Triacontahedron/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5
r_m = (r_i/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/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 Rhombic Triacontahedron - (Measured in Meter) - Midsphere Radius of Rhombic Triacontahedron is the radius of the sphere for which all the edges of the Rhombic Triacontahedron become a tangent line on that sphere.
Insphere Radius of Rhombic Triacontahedron - (Measured in Meter) - Insphere Radius of Rhombic Triacontahedron is the radius of the sphere that is contained by the Rhombic Triacontahedron in such a way that all the faces are just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Rhombic Triacontahedron: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = (r_i/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5 --> (14/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5

Evaluating ... ...

r_m = 14.7204711393357

STEP 3: Convert Result to Output's Unit

14.7204711393357 Meter --> No Conversion Required

FINAL ANSWER

14.7204711393357 ≈ 14.72047 Meter <-- Midsphere Radius of Rhombic Triacontahedron

(Calculation completed in 00.006 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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< Midsphere Radius of Rhombic Triacontahedron Calculators

Midsphere Radius of Rhombic Triacontahedron given Insphere Radius

LaTeX Go Midsphere Radius of Rhombic Triacontahedron = (Insphere Radius of Rhombic Triacontahedron/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5

Midsphere Radius of Rhombic Triacontahedron given Total Surface Area

LaTeX Go Midsphere Radius of Rhombic Triacontahedron = sqrt(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))*(5+sqrt(5))/5

Midsphere Radius of Rhombic Triacontahedron given Volume

LaTeX Go Midsphere Radius of Rhombic Triacontahedron = (Volume of Rhombic Triacontahedron/(4*sqrt(5+2*sqrt(5))))^(1/3)*(5+sqrt(5))/5

Midsphere Radius of Rhombic Triacontahedron

LaTeX Go Midsphere Radius of Rhombic Triacontahedron = Edge Length of Rhombic Triacontahedron/5*(5+sqrt(5))

Midsphere Radius of Rhombic Triacontahedron given Insphere Radius Formula

LaTeX Go

Midsphere Radius of Rhombic Triacontahedron = (Insphere Radius of Rhombic Triacontahedron/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5
r_m = (r_i/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5

What is Rhombic Triacontahedron?

In geometry, the Rhombic Triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron.

How to Calculate Midsphere Radius of Rhombic Triacontahedron given Insphere Radius?

Midsphere Radius of Rhombic Triacontahedron given Insphere Radius calculator uses Midsphere Radius of Rhombic Triacontahedron = (Insphere Radius of Rhombic Triacontahedron/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5 to calculate the Midsphere Radius of Rhombic Triacontahedron, Midsphere Radius of Rhombic Triacontahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Rhombic Triacontahedron become a tangent line on that sphere, calculated using insphere radius of Rhombic Triacontahedron. Midsphere Radius of Rhombic Triacontahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Rhombic Triacontahedron given Insphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Rhombic Triacontahedron given Insphere Radius, enter Insphere Radius of Rhombic Triacontahedron (r_i) and hit the calculate button. Here is how the Midsphere Radius of Rhombic Triacontahedron given Insphere Radius calculation can be explained with given input values -> 14.72047 = (14/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5.

FAQ

What is Midsphere Radius of Rhombic Triacontahedron given Insphere Radius?

Midsphere Radius of Rhombic Triacontahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Rhombic Triacontahedron become a tangent line on that sphere, calculated using insphere radius of Rhombic Triacontahedron and is represented as r_m = (r_i/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5 or Midsphere Radius of Rhombic Triacontahedron = (Insphere Radius of Rhombic Triacontahedron/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5. Insphere Radius of Rhombic Triacontahedron is the radius of the sphere that is contained by the Rhombic Triacontahedron in such a way that all the faces are just touching the sphere.

How to calculate Midsphere Radius of Rhombic Triacontahedron given Insphere Radius?

Midsphere Radius of Rhombic Triacontahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Rhombic Triacontahedron become a tangent line on that sphere, calculated using insphere radius of Rhombic Triacontahedron is calculated using Midsphere Radius of Rhombic Triacontahedron = (Insphere Radius of Rhombic Triacontahedron/sqrt((5+2*sqrt(5))/5))*(5+sqrt(5))/5. To calculate Midsphere Radius of Rhombic Triacontahedron given Insphere Radius, you need Insphere Radius of Rhombic Triacontahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Rhombic Triacontahedron 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 Rhombic Triacontahedron?

In this formula, Midsphere Radius of Rhombic Triacontahedron uses Insphere Radius of Rhombic Triacontahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Midsphere Radius of Rhombic Triacontahedron = Edge Length of Rhombic Triacontahedron/5*(5+sqrt(5))
Midsphere Radius of Rhombic Triacontahedron = (Volume of Rhombic Triacontahedron/(4*sqrt(5+2*sqrt(5))))^(1/3)*(5+sqrt(5))/5
Midsphere Radius of Rhombic Triacontahedron = sqrt(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))*(5+sqrt(5))/5

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