Insphere Radius of Rhombic Triacontahedron given Volume Calculator

✖Volume of Rhombic Triacontahedron is the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron.ⓘ Volume of Rhombic Triacontahedron [V]

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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 Volume [r_i]

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Formula

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Insphere Radius of Rhombic Triacontahedron given Volume

Formula

`"r"_{"i"} = ("V"/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5)`

Example

`"13.75982m"=("12300m³"/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5)`

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Insphere Radius of Rhombic Triacontahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Rhombic Triacontahedron = (Volume of Rhombic Triacontahedron/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5)
r_i = (V/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*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.
Volume of Rhombic Triacontahedron - (Measured in Cubic Meter) - Volume of Rhombic Triacontahedron is the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Rhombic Triacontahedron: 12300 Cubic Meter --> 12300 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (V/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5) --> (12300/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5)

Evaluating ... ...

r_i = 13.7598176604293

STEP 3: Convert Result to Output's Unit

13.7598176604293 Meter --> No Conversion Required

FINAL ANSWER

13.7598176604293 ≈ 13.75982 Meter <-- Insphere Radius of Rhombic Triacontahedron

(Calculation completed in 00.007 seconds)

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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 Volume Formula

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

Insphere Radius of Rhombic Triacontahedron given Volume calculator uses Insphere Radius of Rhombic Triacontahedron = (Volume of Rhombic Triacontahedron/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5) to calculate the Insphere Radius of Rhombic Triacontahedron, Insphere Radius of Rhombic Triacontahedron given Volume 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 volume of Rhombic Triacontahedron. Insphere Radius of Rhombic Triacontahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Rhombic Triacontahedron given Volume using this online calculator? To use this online calculator for Insphere Radius of Rhombic Triacontahedron given Volume, enter Volume of Rhombic Triacontahedron (V) and hit the calculate button. Here is how the Insphere Radius of Rhombic Triacontahedron given Volume calculation can be explained with given input values -> 13.75982 = (12300/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5).

FAQ

What is Insphere Radius of Rhombic Triacontahedron given Volume?

Insphere Radius of Rhombic Triacontahedron given Volume 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 volume of Rhombic Triacontahedron and is represented as r_i = (V/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5) or Insphere Radius of Rhombic Triacontahedron = (Volume of Rhombic Triacontahedron/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5). Volume of Rhombic Triacontahedron is the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron.

How to calculate Insphere Radius of Rhombic Triacontahedron given Volume?

Insphere Radius of Rhombic Triacontahedron given Volume 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 volume of Rhombic Triacontahedron is calculated using Insphere Radius of Rhombic Triacontahedron = (Volume of Rhombic Triacontahedron/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5). To calculate Insphere Radius of Rhombic Triacontahedron given Volume, you need Volume of Rhombic Triacontahedron (V). With our tool, you need to enter the respective value for Volume 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 Volume 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 = (5*Midsphere Radius of Rhombic Triacontahedron)/(5+sqrt(5))*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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