Total Surface Area of Icosahedron given Midsphere Radius Calculator

✖The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Icosahedron [r_m]

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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 Midsphere Radius [TSA]

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Formula

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Total Surface Area of Icosahedron given Midsphere Radius

Formula

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

Example

`"846.8282m²"=5*sqrt(3)*((4*"8m")/(1+sqrt(5)))^2`

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Total Surface Area of Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
TSA = 5*sqrt(3)*((4*r_m)/(1+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.
Midsphere Radius of Icosahedron - (Measured in Meter) - The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Icosahedron: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 5*sqrt(3)*((4*r_m)/(1+sqrt(5)))^2 --> 5*sqrt(3)*((4*8)/(1+sqrt(5)))^2

Evaluating ... ...

TSA = 846.828208959497

STEP 3: Convert Result to Output's Unit

846.828208959497 Square Meter --> No Conversion Required

FINAL ANSWER

846.828208959497 ≈ 846.8282 Square Meter <-- Total Surface Area of Icosahedron

(Calculation completed in 00.020 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 12 Total Surface Area of Icosahedron Calculators

Total Surface Area of Icosahedron given Surface to Volume Ratio

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

Total Surface Area of Icosahedron given Circumsphere Radius

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 Insphere Radius

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

Total Surface Area of Icosahedron given Space Diagonal

Go Total Surface Area of Icosahedron = 5*sqrt(3)*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2

Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length

Go Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2

Total Surface Area of Icosahedron given Midsphere Radius

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

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

Total Surface Area of Icosahedron given Face Perimeter

Go Total Surface Area of Icosahedron = 5*sqrt(3)*(Face Perimeter of Icosahedron/3)^2

Total Surface Area of Icosahedron given Perimeter

Go Total Surface Area of Icosahedron = 5*sqrt(3)*(Perimeter of Icosahedron/30)^2

Total Surface Area of Icosahedron

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

Total Surface Area of Icosahedron given Lateral Surface Area

Go Total Surface Area of Icosahedron = 10/9*Lateral Surface Area of Icosahedron

Total Surface Area of Icosahedron given Face Area

Go Total Surface Area of Icosahedron = 20*Face Area of Icosahedron

Total Surface Area of Icosahedron given Midsphere Radius Formula

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

Total Surface Area of Icosahedron given Midsphere Radius calculator uses Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2 to calculate the Total Surface Area of Icosahedron, The Total Surface Area of Icosahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the midsphere radius of the Icosahedron. Total Surface Area of Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Icosahedron given Midsphere Radius, enter Midsphere Radius of Icosahedron (r_m) and hit the calculate button. Here is how the Total Surface Area of Icosahedron given Midsphere Radius calculation can be explained with given input values -> 846.8282 = 5*sqrt(3)*((4*8)/(1+sqrt(5)))^2.

FAQ

What is Total Surface Area of Icosahedron given Midsphere Radius?

The Total Surface Area of Icosahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the midsphere radius of the Icosahedron and is represented as TSA = 5*sqrt(3)*((4*r_m)/(1+sqrt(5)))^2 or Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2. The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.

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

The Total Surface Area of Icosahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the midsphere radius of the Icosahedron is calculated using Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2. To calculate Total Surface Area of Icosahedron given Midsphere Radius, you need Midsphere Radius of Icosahedron (r_m). With our tool, you need to enter the respective value for Midsphere 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 Midsphere Radius of Icosahedron. We can use 11 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
Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*(Face Perimeter of Icosahedron/3)^2
Total Surface Area of Icosahedron = 20*Face Area of Icosahedron
Total Surface Area of Icosahedron = 10/9*Lateral Surface Area of Icosahedron
Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2
Total Surface Area of Icosahedron = 5*sqrt(3)*(Perimeter of Icosahedron/30)^2

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