Midsphere Radius of Icosidodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
rm = sqrt(5+(2*sqrt(5)))/2*sqrt(TSA/((5*sqrt(3))+(3*sqrt(25+(10*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
Midsphere Radius of Icosidodecahedron - (Measured in Meter) - Midsphere Radius of Icosidodecahedron is the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere.
Total Surface Area of Icosidodecahedron - (Measured in Square Meter) - Total Surface Area of Icosidodecahedron is the total quantity of plane enclosed by the entire surface of the Icosidodecahedron.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Icosidodecahedron: 2900 Square Meter --> 2900 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = sqrt(5+(2*sqrt(5)))/2*sqrt(TSA/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) --> sqrt(5+(2*sqrt(5)))/2*sqrt(2900/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Evaluating ... ...
rm = 15.3078718977268
STEP 3: Convert Result to Output's Unit
15.3078718977268 Meter --> No Conversion Required
FINAL ANSWER
15.3078718977268 15.30787 Meter <-- Midsphere Radius of Icosidodecahedron
(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru
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Walchand College of Engineering (WCE), Sangli
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Midsphere Radius of Icosidodecahedron Calculators

Midsphere Radius of Icosidodecahedron given Total Surface Area
​ LaTeX ​ Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Midsphere Radius of Icosidodecahedron given Volume
​ LaTeX ​ Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)
Midsphere Radius of Icosidodecahedron given Circumsphere Radius
​ LaTeX ​ Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Circumsphere Radius of Icosidodecahedron/(1+sqrt(5))
Midsphere Radius of Icosidodecahedron
​ LaTeX ​ Go Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron

Midsphere Radius of Icosidodecahedron given Total Surface Area Formula

​LaTeX ​Go
Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
rm = sqrt(5+(2*sqrt(5)))/2*sqrt(TSA/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))

What is an Icosidodecahedron?

In geometry, an Icosidodecahedron is a closed and convex polyhedron with 20 (icosi) triangular faces and 12 (dodeca) pentagonal faces. An Icosidodecahedron has 30 identical vertices, with 2 triangles and 2 pentagons meeting at each. And 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

How to Calculate Midsphere Radius of Icosidodecahedron given Total Surface Area?

Midsphere Radius of Icosidodecahedron given Total Surface Area calculator uses Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) to calculate the Midsphere Radius of Icosidodecahedron, Midsphere Radius of Icosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Icosidodecahedron. Midsphere Radius of Icosidodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Icosidodecahedron given Total Surface Area using this online calculator? To use this online calculator for Midsphere Radius of Icosidodecahedron given Total Surface Area, enter Total Surface Area of Icosidodecahedron (TSA) and hit the calculate button. Here is how the Midsphere Radius of Icosidodecahedron given Total Surface Area calculation can be explained with given input values -> 15.30787 = sqrt(5+(2*sqrt(5)))/2*sqrt(2900/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))).

FAQ

What is Midsphere Radius of Icosidodecahedron given Total Surface Area?
Midsphere Radius of Icosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Icosidodecahedron and is represented as rm = sqrt(5+(2*sqrt(5)))/2*sqrt(TSA/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) or Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))). Total Surface Area of Icosidodecahedron is the total quantity of plane enclosed by the entire surface of the Icosidodecahedron.
How to calculate Midsphere Radius of Icosidodecahedron given Total Surface Area?
Midsphere Radius of Icosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Icosidodecahedron is calculated using Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))). To calculate Midsphere Radius of Icosidodecahedron given Total Surface Area, you need Total Surface Area of Icosidodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Icosidodecahedron 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 Icosidodecahedron?
In this formula, Midsphere Radius of Icosidodecahedron uses Total Surface Area of Icosidodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron
  • Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)
  • Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))*Circumsphere Radius of Icosidodecahedron/(1+sqrt(5))
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