Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius Calculator

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

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

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Formula

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Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius

Formula

`"R"_{"A/V"} = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*"r"_{"c"})/(1+sqrt(5))*(45+(17*sqrt(5))))`

Example

`"0.214204m⁻¹"=(6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*"16m")/(1+sqrt(5))*(45+(17*sqrt(5))))`

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Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5))*(45+(17*sqrt(5))))
R_A/V = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*r_c)/(1+sqrt(5))*(45+(17*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 Icosidodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Icosidodecahedron is the numerical ratio of the total surface area of a Icosidodecahedron to the volume of the Icosidodecahedron.
Circumsphere Radius of Icosidodecahedron - (Measured in Meter) - Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Icosidodecahedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*r_c)/(1+sqrt(5))*(45+(17*sqrt(5)))) --> (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*16)/(1+sqrt(5))*(45+(17*sqrt(5))))

Evaluating ... ...

R_A/V = 0.214204344920097

STEP 3: Convert Result to Output's Unit

0.214204344920097 1 per Meter --> No Conversion Required

FINAL ANSWER

0.214204344920097 ≈ 0.214204 1 per Meter <-- Surface to Volume Ratio of Icosidodecahedron

(Calculation completed in 00.004 seconds)

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< 5 Surface to Volume Ratio of Icosidodecahedron Calculators

Surface to Volume Ratio of Icosidodecahedron given Total Surface Area

Go Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))))*(45+(17*sqrt(5))))

Surface to Volume Ratio of Icosidodecahedron given Midsphere Radius

Go Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5))))*(45+(17*sqrt(5))))

Surface to Volume Ratio of Icosidodecahedron given Volume

Go Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)*(45+(17*sqrt(5))))

Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius

Go Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5))*(45+(17*sqrt(5))))

Surface to Volume Ratio of Icosidodecahedron

Go Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Edge Length of Icosidodecahedron*(45+(17*sqrt(5))))

Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius Formula

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 Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius?

Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius calculator uses Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5))*(45+(17*sqrt(5)))) to calculate the Surface to Volume Ratio of Icosidodecahedron, Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Icosidodecahedron to the volume of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron. Surface to Volume Ratio of Icosidodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius, enter Circumsphere Radius of Icosidodecahedron (r_c) and hit the calculate button. Here is how the Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius calculation can be explained with given input values -> 0.214204 = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*16)/(1+sqrt(5))*(45+(17*sqrt(5)))).

FAQ

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

Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Icosidodecahedron to the volume of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron and is represented as R_A/V = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*r_c)/(1+sqrt(5))*(45+(17*sqrt(5)))) or Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5))*(45+(17*sqrt(5)))). Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.

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

Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Icosidodecahedron to the volume of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron is calculated using Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5))*(45+(17*sqrt(5)))). To calculate Surface to Volume Ratio of Icosidodecahedron given Circumsphere Radius, you need Circumsphere Radius of Icosidodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Surface to Volume Ratio of Icosidodecahedron?

In this formula, Surface to Volume Ratio of Icosidodecahedron uses Circumsphere Radius of Icosidodecahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Edge Length of Icosidodecahedron*(45+(17*sqrt(5))))
Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))))*(45+(17*sqrt(5))))
Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)*(45+(17*sqrt(5))))
Surface to Volume Ratio of Icosidodecahedron = (6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5))))*(45+(17*sqrt(5))))

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