Midsphere Radius of Rhombicosidodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*Edge Length of Rhombicosidodecahedron
rm = sqrt(10+(4*sqrt(5)))/2*le
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 Rhombicosidodecahedron - (Measured in Meter) - Midsphere Radius of Rhombicosidodecahedron is the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere.
Edge Length of Rhombicosidodecahedron - (Measured in Meter) - Edge Length of Rhombicosidodecahedron is the length of any edge of the Rhombicosidodecahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Rhombicosidodecahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = sqrt(10+(4*sqrt(5)))/2*le --> sqrt(10+(4*sqrt(5)))/2*10
Evaluating ... ...
rm = 21.7625089948282
STEP 3: Convert Result to Output's Unit
21.7625089948282 Meter --> No Conversion Required
FINAL ANSWER
21.7625089948282 21.76251 Meter <-- Midsphere Radius of Rhombicosidodecahedron
(Calculation completed in 00.006 seconds)

Credits

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St Joseph's College (SJC), Bengaluru
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Indian Institute of Information Technology (IIIT), Bhopal
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5 Midsphere Radius of Rhombicosidodecahedron Calculators

Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Rhombicosidodecahedron*(60+(29*sqrt(5))))
Midsphere Radius of Rhombicosidodecahedron given Total Surface Area
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Midsphere Radius of Rhombicosidodecahedron given Circumsphere Radius
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))*Circumsphere Radius of Rhombicosidodecahedron/(sqrt(11+(4*sqrt(5))))
Midsphere Radius of Rhombicosidodecahedron given Volume
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*((3*Volume of Rhombicosidodecahedron)/(60+(29*sqrt(5))))^(1/3)
Midsphere Radius of Rhombicosidodecahedron
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*Edge Length of Rhombicosidodecahedron

Midsphere Radius of Rhombicosidodecahedron Formula

Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*Edge Length of Rhombicosidodecahedron
rm = sqrt(10+(4*sqrt(5)))/2*le

What is a Rhombicosidodecahedron?

In geometry, the Rhombicosidodecahedron, is an Archimedean solid, one of the 13 convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges. If you expand an icosahedron by moving the faces away from the origin the right amount, without changing the orientation or size of the faces, and do the same to its dual dodecahedron, and patch the square holes in the result, you get a Rhombicosidodecahedron. Therefore, it has the same number of triangles as an icosahedron and the same number of pentagons as a dodecahedron, with a square for each edge of either.

How to Calculate Midsphere Radius of Rhombicosidodecahedron?

Midsphere Radius of Rhombicosidodecahedron calculator uses Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*Edge Length of Rhombicosidodecahedron to calculate the Midsphere Radius of Rhombicosidodecahedron, Midsphere Radius of Rhombicosidodecahedron formula is defined as the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere. Midsphere Radius of Rhombicosidodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Rhombicosidodecahedron using this online calculator? To use this online calculator for Midsphere Radius of Rhombicosidodecahedron, enter Edge Length of Rhombicosidodecahedron (le) and hit the calculate button. Here is how the Midsphere Radius of Rhombicosidodecahedron calculation can be explained with given input values -> 21.76251 = sqrt(10+(4*sqrt(5)))/2*10.

FAQ

What is Midsphere Radius of Rhombicosidodecahedron?
Midsphere Radius of Rhombicosidodecahedron formula is defined as the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere and is represented as rm = sqrt(10+(4*sqrt(5)))/2*le or Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*Edge Length of Rhombicosidodecahedron. Edge Length of Rhombicosidodecahedron is the length of any edge of the Rhombicosidodecahedron.
How to calculate Midsphere Radius of Rhombicosidodecahedron?
Midsphere Radius of Rhombicosidodecahedron formula is defined as the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere is calculated using Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*Edge Length of Rhombicosidodecahedron. To calculate Midsphere Radius of Rhombicosidodecahedron, you need Edge Length of Rhombicosidodecahedron (le). With our tool, you need to enter the respective value for Edge Length of Rhombicosidodecahedron 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 Rhombicosidodecahedron?
In this formula, Midsphere Radius of Rhombicosidodecahedron uses Edge Length of Rhombicosidodecahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
  • Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*((3*Volume of Rhombicosidodecahedron)/(60+(29*sqrt(5))))^(1/3)
  • Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))*Circumsphere Radius of Rhombicosidodecahedron/(sqrt(11+(4*sqrt(5))))
  • Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Rhombicosidodecahedron*(60+(29*sqrt(5))))
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