Insphere Radius of Rhombic Triacontahedron given Midsphere Radius Calculator

✖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 [r_m]

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✖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 given Midsphere Radius [r_i]

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Formula

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Insphere Radius of Rhombic Triacontahedron given Midsphere Radius

Formula

`"r"_{"i"} = (5*"r"_{"m"})/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5)`

Example

`"14.26585m"=(5*"15m")/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5)`

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Insphere Radius of Rhombic Triacontahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Rhombic Triacontahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (5*r_m)/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5) --> (5*15)/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5)

Evaluating ... ...

r_i = 14.2658477444273

STEP 3: Convert Result to Output's Unit

14.2658477444273 Meter --> No Conversion Required

FINAL ANSWER

14.2658477444273 ≈ 14.26585 Meter <-- Insphere Radius of Rhombic Triacontahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

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< 4 Insphere Radius of Rhombic Triacontahedron Calculators

Insphere Radius of Rhombic Triacontahedron given Volume

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

Insphere Radius of Rhombic Triacontahedron given Total Surface Area

Go Insphere Radius of Rhombic Triacontahedron = sqrt(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5)

Insphere Radius of Rhombic Triacontahedron given Midsphere Radius

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

Insphere Radius of Rhombic Triacontahedron

Go Insphere Radius of Rhombic Triacontahedron = Edge Length of Rhombic Triacontahedron*sqrt((5+(2*sqrt(5)))/5)

Insphere Radius of Rhombic Triacontahedron given Midsphere Radius Formula

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

Insphere Radius of Rhombic Triacontahedron given Midsphere Radius calculator uses Insphere Radius of Rhombic Triacontahedron = (5*Midsphere Radius of Rhombic Triacontahedron)/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5) to calculate the Insphere Radius of Rhombic Triacontahedron, Insphere Radius of Rhombic Triacontahedron given Midsphere Radius formula is defined as 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, calculated using midsphere radius of Rhombic Triacontahedron. Insphere Radius of Rhombic Triacontahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Rhombic Triacontahedron given Midsphere Radius using this online calculator? To use this online calculator for Insphere Radius of Rhombic Triacontahedron given Midsphere Radius, enter Midsphere Radius of Rhombic Triacontahedron (r_m) and hit the calculate button. Here is how the Insphere Radius of Rhombic Triacontahedron given Midsphere Radius calculation can be explained with given input values -> 14.26585 = (5*15)/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5).

FAQ

What is Insphere Radius of Rhombic Triacontahedron given Midsphere Radius?

Insphere Radius of Rhombic Triacontahedron given Midsphere Radius formula is defined as 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, calculated using midsphere radius of Rhombic Triacontahedron and is represented as r_i = (5*r_m)/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5) or Insphere Radius of Rhombic Triacontahedron = (5*Midsphere Radius of Rhombic Triacontahedron)/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5). 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.

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

Insphere Radius of Rhombic Triacontahedron given Midsphere Radius formula is defined as 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, calculated using midsphere radius of Rhombic Triacontahedron is calculated using Insphere Radius of Rhombic Triacontahedron = (5*Midsphere Radius of Rhombic Triacontahedron)/(5+sqrt(5))*sqrt((5+(2*sqrt(5)))/5). To calculate Insphere Radius of Rhombic Triacontahedron given Midsphere Radius, you need Midsphere Radius of Rhombic Triacontahedron (r_m). With our tool, you need to enter the respective value for Midsphere 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 Insphere Radius of Rhombic Triacontahedron?

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

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

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