Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Rhombicosidodecahedron is the numerical ratio of the total surface area of a Rhombicosidodecahedron to the volume of the Rhombicosidodecahedron.ⓘ Surface to Volume Ratio of Rhombicosidodecahedron [R_A/V]

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✖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.ⓘ Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio [r_m]

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Formula

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Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio

Formula

`"r"_{"m"} = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/("R"_{"A/V"}*(60+(29*sqrt(5))))`

Example

`"31.01374m"=sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/("0.1m⁻¹"*(60+(29*sqrt(5))))`

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Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
r_m = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(R_A/V*(60+(29*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 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.
Surface to Volume Ratio of Rhombicosidodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Rhombicosidodecahedron is the numerical ratio of the total surface area of a Rhombicosidodecahedron to the volume of the Rhombicosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Rhombicosidodecahedron: 0.1 1 per Meter --> 0.1 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(R_A/V*(60+(29*sqrt(5)))) --> sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(0.1*(60+(29*sqrt(5))))

Evaluating ... ...

r_m = 31.0137436838189

STEP 3: Convert Result to Output's Unit

31.0137436838189 Meter --> No Conversion Required

FINAL ANSWER

31.0137436838189 ≈ 31.01374 Meter <-- Midsphere Radius of Rhombicosidodecahedron

(Calculation completed in 00.004 seconds)

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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 given Surface to Volume Ratio Formula

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 given Surface to Volume Ratio?

Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio calculator uses 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)))) to calculate the Midsphere Radius of Rhombicosidodecahedron, Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio 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 calculated using the surface to volume ratio of the Rhombicosidodecahedron. Midsphere Radius of Rhombicosidodecahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Rhombicosidodecahedron (R_A/V) and hit the calculate button. Here is how the Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 31.01374 = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(0.1*(60+(29*sqrt(5)))).

FAQ

What is Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio?

Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio 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 calculated using the surface to volume ratio of the Rhombicosidodecahedron and is represented as r_m = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(R_A/V*(60+(29*sqrt(5)))) or 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)))). Surface to Volume Ratio of Rhombicosidodecahedron is the numerical ratio of the total surface area of a Rhombicosidodecahedron to the volume of the Rhombicosidodecahedron.

How to calculate Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio?

Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio 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 calculated using the surface to volume ratio of the Rhombicosidodecahedron is calculated using 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)))). To calculate Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Rhombicosidodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio 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*Edge Length of Rhombicosidodecahedron
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))))

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