Midsphere Radius of Icosahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
rm = (1+sqrt(5))/4*sqrt(TSA/(5*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.
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.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Icosahedron: 870 Square Meter --> 870 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = (1+sqrt(5))/4*sqrt(TSA/(5*sqrt(3))) --> (1+sqrt(5))/4*sqrt(870/(5*sqrt(3)))
Evaluating ... ...
rm = 8.1087134814733
STEP 3: Convert Result to Output's Unit
8.1087134814733 Meter --> No Conversion Required
FINAL ANSWER
8.1087134814733 8.108713 Meter <-- Midsphere Radius of Icosahedron
(Calculation completed in 00.004 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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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 Total Surface Area Formula

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

Midsphere Radius of Icosahedron given Total Surface Area calculator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))) to calculate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Total Surface 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 total surface area of the Icosahedron. Midsphere Radius of Icosahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Icosahedron given Total Surface Area using this online calculator? To use this online calculator for Midsphere Radius of Icosahedron given Total Surface Area, enter Total Surface Area of Icosahedron (TSA) and hit the calculate button. Here is how the Midsphere Radius of Icosahedron given Total Surface Area calculation can be explained with given input values -> 8.108713 = (1+sqrt(5))/4*sqrt(870/(5*sqrt(3))).

FAQ

What is Midsphere Radius of Icosahedron given Total Surface Area?
The Midsphere Radius of Icosahedron given Total Surface 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 total surface area of the Icosahedron and is represented as rm = (1+sqrt(5))/4*sqrt(TSA/(5*sqrt(3))) or Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))). Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.
How to calculate Midsphere Radius of Icosahedron given Total Surface Area?
The Midsphere Radius of Icosahedron given Total Surface 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 total surface area of the Icosahedron is calculated using Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))). To calculate Midsphere Radius of Icosahedron given Total Surface Area, you need Total Surface Area of Icosahedron (TSA). With our tool, you need to enter the respective value for Total Surface 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 Total Surface 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*((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((4*Face Area of Icosahedron)/sqrt(3))
  • 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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