Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Rhombicosidodecahedron is the radius of the sphere that contains the Rhombicosidodecahedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Rhombicosidodecahedron [r_c]

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✖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 given Circumsphere Radius [R_A/V]

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Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Rhombicosidodecahedron)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5))))
R_A/V = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*r_c)/(sqrt(11+(4*sqrt(5))))*(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

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.
Circumsphere Radius of Rhombicosidodecahedron - (Measured in Meter) - Circumsphere Radius of Rhombicosidodecahedron is the radius of the sphere that contains the Rhombicosidodecahedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Rhombicosidodecahedron: 22 Meter --> 22 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*r_c)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5)))) --> (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*22)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5))))

Evaluating ... ...

R_A/V = 0.144644407361571

STEP 3: Convert Result to Output's Unit

0.144644407361571 1 per Meter --> No Conversion Required

FINAL ANSWER

0.144644407361571 ≈ 0.144644 1 per Meter <-- Surface to Volume Ratio of Rhombicosidodecahedron

(Calculation completed in 00.004 seconds)

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< Surface to Volume Ratio of Rhombicosidodecahedron Calculators

Surface to Volume Ratio of Rhombicosidodecahedron given Total Surface Area

LaTeX Go Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))*(60+(29*sqrt(5))))

Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius

LaTeX Go Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Rhombicosidodecahedron)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5))))

Surface to Volume Ratio of Rhombicosidodecahedron given Volume

LaTeX Go Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(((3*Volume of Rhombicosidodecahedron)/(60+(29*sqrt(5))))^(1/3)*(60+(29*sqrt(5))))

Surface to Volume Ratio of Rhombicosidodecahedron

LaTeX Go Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Edge Length of Rhombicosidodecahedron*(60+(29*sqrt(5))))

Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius Formula

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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 Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius?

Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius calculator uses Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Rhombicosidodecahedron)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5)))) to calculate the Surface to Volume Ratio of Rhombicosidodecahedron, Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Rhombicosidodecahedron to the volume of the Rhombicosidodecahedron, and calculated using the circumsphere radius of the Rhombicosidodecahedron. Surface to Volume Ratio of Rhombicosidodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius, enter Circumsphere Radius of Rhombicosidodecahedron (r_c) and hit the calculate button. Here is how the Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius calculation can be explained with given input values -> 0.144644 = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*22)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5)))).

FAQ

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

Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Rhombicosidodecahedron to the volume of the Rhombicosidodecahedron, and calculated using the circumsphere radius of the Rhombicosidodecahedron and is represented as R_A/V = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*r_c)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5)))) or Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Rhombicosidodecahedron)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5)))). Circumsphere Radius of Rhombicosidodecahedron is the radius of the sphere that contains the Rhombicosidodecahedron in such a way that all the vertices are lying on the sphere.

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

Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Rhombicosidodecahedron to the volume of the Rhombicosidodecahedron, and calculated using the circumsphere radius of the Rhombicosidodecahedron is calculated using Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Rhombicosidodecahedron)/(sqrt(11+(4*sqrt(5))))*(60+(29*sqrt(5)))). To calculate Surface to Volume Ratio of Rhombicosidodecahedron given Circumsphere Radius, you need Circumsphere Radius of Rhombicosidodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Surface to Volume Ratio of Rhombicosidodecahedron?

In this formula, Surface to Volume Ratio of Rhombicosidodecahedron uses Circumsphere Radius of Rhombicosidodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Edge Length of Rhombicosidodecahedron*(60+(29*sqrt(5))))
Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))*(60+(29*sqrt(5))))
Surface to Volume Ratio of Rhombicosidodecahedron = (3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(((3*Volume of Rhombicosidodecahedron)/(60+(29*sqrt(5))))^(1/3)*(60+(29*sqrt(5))))

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