Total Surface Area of Icosahedron given Insphere Radius Calculator

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

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✖Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.ⓘ Total Surface Area of Icosahedron given Insphere Radius [TSA]

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Total Surface Area of Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
TSA = 5*sqrt(3)*((12*r_i)/(sqrt(3)*(3+sqrt(5))))^2
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 Icosahedron - (Measured in Square Meter) - Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.
Insphere Radius of Icosahedron - (Measured in Meter) - Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Icosahedron: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 5*sqrt(3)*((12*r_i)/(sqrt(3)*(3+sqrt(5))))^2 --> 5*sqrt(3)*((12*7)/(sqrt(3)*(3+sqrt(5))))^2

Evaluating ... ...

TSA = 742.946253109039

STEP 3: Convert Result to Output's Unit

742.946253109039 Square Meter --> No Conversion Required

FINAL ANSWER

742.946253109039 ≈ 742.9463 Square Meter <-- Total Surface Area of Icosahedron

(Calculation completed in 00.004 seconds)

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< Total Surface Area of Icosahedron Calculators

Total Surface Area of Icosahedron given Circumsphere Radius

LaTeX Go Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2

Total Surface Area of Icosahedron given Midsphere Radius

LaTeX Go Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2

Total Surface Area of Icosahedron given Volume

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

Total Surface Area of Icosahedron

LaTeX Go Total Surface Area of Icosahedron = 5*sqrt(3)*Edge Length of Icosahedron^2

Total Surface Area of Icosahedron given Insphere Radius Formula

LaTeX Go

Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
TSA = 5*sqrt(3)*((12*r_i)/(sqrt(3)*(3+sqrt(5))))^2

What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Total Surface Area of Icosahedron given Insphere Radius?

Total Surface Area of Icosahedron given Insphere Radius calculator uses Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2 to calculate the Total Surface Area of Icosahedron, The Total Surface Area of Icosahedron given Insphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the insphere radius of the Icosahedron. Total Surface Area of Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Total Surface Area of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (r_i) and hit the calculate button. Here is how the Total Surface Area of Icosahedron given Insphere Radius calculation can be explained with given input values -> 742.9463 = 5*sqrt(3)*((12*7)/(sqrt(3)*(3+sqrt(5))))^2.

FAQ

What is Total Surface Area of Icosahedron given Insphere Radius?

The Total Surface Area of Icosahedron given Insphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the insphere radius of the Icosahedron and is represented as TSA = 5*sqrt(3)*((12*r_i)/(sqrt(3)*(3+sqrt(5))))^2 or Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2. Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.

How to calculate Total Surface Area of Icosahedron given Insphere Radius?

The Total Surface Area of Icosahedron given Insphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the insphere radius of the Icosahedron is calculated using Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2. To calculate Total Surface Area of Icosahedron given Insphere Radius, you need Insphere Radius of Icosahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Icosahedron 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 Icosahedron?

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

Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(2/3)
Total Surface Area of Icosahedron = 5*sqrt(3)*Edge Length of Icosahedron^2

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