Midsphere Radius of Icosidodecahedron Calculator

✖Edge Length of Icosidodecahedron is the length of any edge of the Icosidodecahedron.ⓘ Edge Length of Icosidodecahedron [l_e]

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✖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.ⓘ Midsphere Radius of Icosidodecahedron [r_m]

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Midsphere Radius of Icosidodecahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron
r_m = sqrt(5+(2*sqrt(5)))/2*l_e
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.
Edge Length of Icosidodecahedron - (Measured in Meter) - Edge Length of Icosidodecahedron is the length of any edge of the Icosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Icosidodecahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = sqrt(5+(2*sqrt(5)))/2*l_e --> sqrt(5+(2*sqrt(5)))/2*10

Evaluating ... ...

r_m = 15.3884176858763

STEP 3: Convert Result to Output's Unit

15.3884176858763 Meter --> No Conversion Required

FINAL ANSWER

15.3884176858763 ≈ 15.38842 Meter <-- Midsphere Radius of Icosidodecahedron

(Calculation completed in 00.008 seconds)

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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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< 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 Formula

LaTeX Go

Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron
r_m = sqrt(5+(2*sqrt(5)))/2*l_e

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?

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

How to calculate Midsphere Radius of Icosidodecahedron using this online calculator? To use this online calculator for Midsphere Radius of Icosidodecahedron, enter Edge Length of Icosidodecahedron (l_e) and hit the calculate button. Here is how the Midsphere Radius of Icosidodecahedron calculation can be explained with given input values -> 15.38842 = sqrt(5+(2*sqrt(5)))/2*10.

FAQ

What is Midsphere Radius of Icosidodecahedron?

Midsphere Radius of Icosidodecahedron 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 is represented as r_m = sqrt(5+(2*sqrt(5)))/2*l_e or Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron. Edge Length of Icosidodecahedron is the length of any edge of the Icosidodecahedron.

How to calculate Midsphere Radius of Icosidodecahedron?

Midsphere Radius of Icosidodecahedron formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere is calculated using Midsphere Radius of Icosidodecahedron = sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron. To calculate Midsphere Radius of Icosidodecahedron, you need Edge Length of Icosidodecahedron (l_e). With our tool, you need to enter the respective value for Edge Length 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 Edge Length 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*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
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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