Total Surface Area 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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✖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 given Insphere Radius [TSA]

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Total Surface Area of Rhombic Triacontahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

TSA = 12*(r_i/sqrt((5+(2*sqrt(5)))/5))^2*sqrt(5) --> 12*(14/sqrt((5+(2*sqrt(5)))/5))^2*sqrt(5)

Evaluating ... ...

TSA = 2776.15941539753

STEP 3: Convert Result to Output's Unit

2776.15941539753 Square Meter --> No Conversion Required

FINAL ANSWER

2776.15941539753 ≈ 2776.159 Square Meter <-- Total Surface Area of Rhombic Triacontahedron

(Calculation completed in 00.007 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Vellore Institute of Technology (VIT), Bhopal

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< Total Surface Area of Rhombic Triacontahedron Calculators

Total Surface Area of Rhombic Triacontahedron given Insphere Radius

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

Total Surface Area of Rhombic Triacontahedron given Volume

LaTeX Go Total Surface Area of Rhombic Triacontahedron = 12*((Volume of Rhombic Triacontahedron)/(4*sqrt(5+(2*sqrt(5)))))^(2/3)*sqrt(5)

Total Surface Area of Rhombic Triacontahedron given Midsphere Radius

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

Total Surface Area of Rhombic Triacontahedron

LaTeX Go Total Surface Area of Rhombic Triacontahedron = 12*Edge Length of Rhombic Triacontahedron^2*sqrt(5)

Total Surface Area of Rhombic Triacontahedron given Insphere Radius Formula

LaTeX Go

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

Total Surface Area of Rhombic Triacontahedron given Insphere Radius calculator uses Total Surface Area of Rhombic Triacontahedron = 12*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^2*sqrt(5) to calculate the Total Surface Area of Rhombic Triacontahedron, Total Surface Area of Rhombic Triacontahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Rhombic Triacontahedron, calculated using insphere radius of Rhombic Triacontahedron. Total Surface Area of Rhombic Triacontahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Rhombic Triacontahedron given Insphere Radius using this online calculator? To use this online calculator for Total Surface Area of Rhombic Triacontahedron given Insphere Radius, enter Insphere Radius of Rhombic Triacontahedron (r_i) and hit the calculate button. Here is how the Total Surface Area of Rhombic Triacontahedron given Insphere Radius calculation can be explained with given input values -> 2776.159 = 12*(14/sqrt((5+(2*sqrt(5)))/5))^2*sqrt(5).

FAQ

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

Total Surface Area of Rhombic Triacontahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Rhombic Triacontahedron, calculated using insphere radius of Rhombic Triacontahedron and is represented as TSA = 12*(r_i/sqrt((5+(2*sqrt(5)))/5))^2*sqrt(5) or Total Surface Area of Rhombic Triacontahedron = 12*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^2*sqrt(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 Total Surface Area of Rhombic Triacontahedron given Insphere Radius?

Total Surface Area of Rhombic Triacontahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Rhombic Triacontahedron, calculated using insphere radius of Rhombic Triacontahedron is calculated using Total Surface Area of Rhombic Triacontahedron = 12*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^2*sqrt(5). To calculate Total Surface Area 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 Total Surface Area of Rhombic Triacontahedron?

In this formula, Total Surface Area 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 -

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

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