Midsphere Radius of Icosahedron given Face Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
rm = (1+sqrt(5))/4*sqrt((4*AFace)/sqrt(3))
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
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.
Face Area of Icosahedron - (Measured in Square Meter) - The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Face Area of Icosahedron: 45 Square Meter --> 45 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = (1+sqrt(5))/4*sqrt((4*AFace)/sqrt(3)) --> (1+sqrt(5))/4*sqrt((4*45)/sqrt(3))
Evaluating ... ...
rm = 8.24733400965763
STEP 3: Convert Result to Output's Unit
8.24733400965763 Meter --> No Conversion Required
FINAL ANSWER
8.24733400965763 8.247334 Meter <-- Midsphere Radius of Icosahedron
(Calculation completed in 00.006 seconds)

Credits

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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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Mumbai University (DJSCE), Mumbai
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11 Midsphere Radius of Icosahedron Calculators

Midsphere Radius of Icosahedron given Surface to Volume Ratio
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Midsphere Radius of Icosahedron given Lateral Surface Area
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Midsphere Radius of Icosahedron given Circumsphere Radius
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5))))
Midsphere Radius of Icosahedron given Insphere Radius
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Midsphere Radius of Icosahedron given Total Surface Area
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Midsphere Radius of Icosahedron given Space Diagonal
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))
Midsphere Radius of Icosahedron given Face Area
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Midsphere Radius of Icosahedron given Volume
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)
Midsphere Radius of Icosahedron given Face Perimeter
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))*Face Perimeter of Icosahedron/12
Midsphere Radius of Icosahedron given Perimeter
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))*Perimeter of Icosahedron/120
Midsphere Radius of Icosahedron
​ Go Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron

Midsphere Radius of Icosahedron given Face Area Formula

Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
rm = (1+sqrt(5))/4*sqrt((4*AFace)/sqrt(3))

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 Midsphere Radius of Icosahedron given Face Area?

Midsphere Radius of Icosahedron given Face Area calculator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)) to calculate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Face Area formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the face area of the Icosahedron. Midsphere Radius of Icosahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Icosahedron given Face Area using this online calculator? To use this online calculator for Midsphere Radius of Icosahedron given Face Area, enter Face Area of Icosahedron (AFace) and hit the calculate button. Here is how the Midsphere Radius of Icosahedron given Face Area calculation can be explained with given input values -> 8.247334 = (1+sqrt(5))/4*sqrt((4*45)/sqrt(3)).

FAQ

What is Midsphere Radius of Icosahedron given Face Area?
The Midsphere Radius of Icosahedron given Face Area formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the face area of the Icosahedron and is represented as rm = (1+sqrt(5))/4*sqrt((4*AFace)/sqrt(3)) or Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)). The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.
How to calculate Midsphere Radius of Icosahedron given Face Area?
The Midsphere Radius of Icosahedron given Face Area formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the face area of the Icosahedron is calculated using Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)). To calculate Midsphere Radius of Icosahedron given Face Area, you need Face Area of Icosahedron (AFace). With our tool, you need to enter the respective value for Face Area 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 Midsphere Radius of Icosahedron?
In this formula, Midsphere Radius of Icosahedron uses Face Area of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron
  • Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5))))
  • Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
  • Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))
  • Midsphere Radius of Icosahedron = (1+sqrt(5))*(3*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
  • Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
  • Midsphere Radius of Icosahedron = (1+sqrt(5))/4*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)
  • Midsphere Radius of Icosahedron = (1+sqrt(5))*Face Perimeter of Icosahedron/12
  • Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
  • Midsphere Radius of Icosahedron = (1+sqrt(5))*Perimeter of Icosahedron/120
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