Insphere Radius of Rhombic Triacontahedron given Total Surface Area Calculator

✖Total Surface Area of Rhombic Triacontahedron is the total quantity of plane enclosed on the entire surface of the Rhombic Triacontahedron.ⓘ Total Surface Area of Rhombic Triacontahedron [TSA]

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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 Total Surface Area [r_i]

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Formula

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Insphere Radius of Rhombic Triacontahedron given Total Surface Area

Formula

`"r"_{"i"} = sqrt("TSA"/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5)`

Example

`"13.80663m"=sqrt("2700m²"/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5)`

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Insphere Radius of Rhombic Triacontahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Rhombic Triacontahedron = sqrt(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5)
r_i = sqrt(TSA/(12*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.
Total Surface Area of Rhombic Triacontahedron - (Measured in Square Meter) - Total Surface Area of Rhombic Triacontahedron is the total quantity of plane enclosed on the entire surface of the Rhombic Triacontahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Rhombic Triacontahedron: 2700 Square Meter --> 2700 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = sqrt(TSA/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5) --> sqrt(2700/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5)

Evaluating ... ...

r_i = 13.8066309788989

STEP 3: Convert Result to Output's Unit

13.8066309788989 Meter --> No Conversion Required

FINAL ANSWER

13.8066309788989 ≈ 13.80663 Meter <-- Insphere Radius of Rhombic Triacontahedron

(Calculation completed in 00.004 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 Total Surface Area Formula

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

Insphere Radius of Rhombic Triacontahedron given Total Surface Area calculator uses Insphere Radius of Rhombic Triacontahedron = sqrt(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5) to calculate the Insphere Radius of Rhombic Triacontahedron, Insphere Radius of Rhombic Triacontahedron given Total Surface Area 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 total surface area of Rhombic Triacontahedron. Insphere Radius of Rhombic Triacontahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Rhombic Triacontahedron given Total Surface Area using this online calculator? To use this online calculator for Insphere Radius of Rhombic Triacontahedron given Total Surface Area, enter Total Surface Area of Rhombic Triacontahedron (TSA) and hit the calculate button. Here is how the Insphere Radius of Rhombic Triacontahedron given Total Surface Area calculation can be explained with given input values -> 13.80663 = sqrt(2700/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5).

FAQ

What is Insphere Radius of Rhombic Triacontahedron given Total Surface Area?

Insphere Radius of Rhombic Triacontahedron given Total Surface Area 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 total surface area of Rhombic Triacontahedron and is represented as r_i = sqrt(TSA/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5) or Insphere Radius of Rhombic Triacontahedron = sqrt(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5). Total Surface Area of Rhombic Triacontahedron is the total quantity of plane enclosed on the entire surface of the Rhombic Triacontahedron.

How to calculate Insphere Radius of Rhombic Triacontahedron given Total Surface Area?

Insphere Radius of Rhombic Triacontahedron given Total Surface Area 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 total surface area of Rhombic Triacontahedron is calculated using Insphere Radius of Rhombic Triacontahedron = sqrt(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))*sqrt((5+(2*sqrt(5)))/5). To calculate Insphere Radius of Rhombic Triacontahedron given Total Surface Area, you need Total Surface Area of Rhombic Triacontahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area 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 Total Surface Area 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 = (Volume of Rhombic Triacontahedron/(4*sqrt(5+(2*sqrt(5)))))^(1/3)*sqrt((5+(2*sqrt(5)))/5)

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