Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius Calculator

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

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

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Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

SA:V of Truncated Icosidodecahedron = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(Circumsphere Radius of Truncated Icosidodecahedron/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5))))
R_A/V = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(r_c/(sqrt(31+(12*sqrt(5))))*(19+(10*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

SA:V of Truncated Icosidodecahedron - (Measured in 1 per Meter) - SA:V of Truncated Icosidodecahedron is the numerical ratio of the total surface area of a Truncated Icosidodecahedron to the volume of the Truncated Icosidodecahedron.
Circumsphere Radius of Truncated Icosidodecahedron - (Measured in Meter) - Circumsphere Radius of Truncated Icosidodecahedron is the radius of the sphere that contains the Truncated 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 Truncated Icosidodecahedron: 38 Meter --> 38 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(r_c/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5)))) --> (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(38/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5))))

Evaluating ... ...

R_A/V = 0.0843322006294514

STEP 3: Convert Result to Output's Unit

0.0843322006294514 1 per Meter --> No Conversion Required

FINAL ANSWER

0.0843322006294514 ≈ 0.084332 1 per Meter <-- SA:V of Truncated Icosidodecahedron

(Calculation completed in 00.020 seconds)

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< Surface to Volume Ratio of Truncated Icosidodecahedron Calculators

Surface to Volume Ratio of Truncated Icosidodecahedron given Total Surface Area

LaTeX Go SA:V of Truncated Icosidodecahedron = (6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))*(19+(10*sqrt(5))))

Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius

LaTeX Go SA:V of Truncated Icosidodecahedron = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(Circumsphere Radius of Truncated Icosidodecahedron/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5))))

Surface to Volume Ratio of Truncated Icosidodecahedron given Volume

LaTeX Go SA:V of Truncated Icosidodecahedron = (6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/((Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3)*(19+(10*sqrt(5))))

Surface to Volume Ratio of Truncated Icosidodecahedron

LaTeX Go SA:V of Truncated Icosidodecahedron = (6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(Edge Length of Truncated Icosidodecahedron*(19+(10*sqrt(5))))

Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius Formula

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What is a Truncated Icosidodecahedron?

In geometry, the Truncated Icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal non-prismatic solids constructed by two or more types of regular polygon faces. It has 62 faces which include 30 squares, 20 regular hexagons and 12 regular decagons. Each vertex is identical in such a way that, one square, one hexagon and one decagon join at each vertex. It has the most edges and vertices of all Platonic and Archimedean solids, though the snub dodecahedron has more number of faces. Out of all vertex-transitive polyhedra, it occupies the largest percentage (89.80%) of the volume of a sphere in which it is inscribed, very narrowly beating the Snub Dodecahedron (89.63%) and Small Rhombicosidodecahedron (89.23%), and less narrowly beating the Truncated Icosahedron (86.74%).

How to Calculate Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius?

Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius calculator uses SA:V of Truncated Icosidodecahedron = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(Circumsphere Radius of Truncated Icosidodecahedron/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5)))) to calculate the SA:V of Truncated Icosidodecahedron, Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Truncated Icosidodecahedron to the volume of the Truncated Icosidodecahedron, and calculated using the circumsphere radius of the Truncated Icosidodecahedron. SA:V of Truncated Icosidodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius, enter Circumsphere Radius of Truncated Icosidodecahedron (r_c) and hit the calculate button. Here is how the Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius calculation can be explained with given input values -> 0.084332 = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(38/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5)))).

FAQ

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

Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Truncated Icosidodecahedron to the volume of the Truncated Icosidodecahedron, and calculated using the circumsphere radius of the Truncated Icosidodecahedron and is represented as R_A/V = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(r_c/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5)))) or SA:V of Truncated Icosidodecahedron = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(Circumsphere Radius of Truncated Icosidodecahedron/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5)))). Circumsphere Radius of Truncated Icosidodecahedron is the radius of the sphere that contains the Truncated Icosidodecahedron in such a way that all the vertices are lying on the sphere.

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

Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Truncated Icosidodecahedron to the volume of the Truncated Icosidodecahedron, and calculated using the circumsphere radius of the Truncated Icosidodecahedron is calculated using SA:V of Truncated Icosidodecahedron = (3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(Circumsphere Radius of Truncated Icosidodecahedron/(sqrt(31+(12*sqrt(5))))*(19+(10*sqrt(5)))). To calculate Surface to Volume Ratio of Truncated Icosidodecahedron given Circumsphere Radius, you need Circumsphere Radius of Truncated Icosidodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Truncated 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 SA:V of Truncated Icosidodecahedron?

In this formula, SA:V of Truncated Icosidodecahedron uses Circumsphere Radius of Truncated Icosidodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

SA:V of Truncated Icosidodecahedron = (6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(Edge Length of Truncated Icosidodecahedron*(19+(10*sqrt(5))))
SA:V of Truncated Icosidodecahedron = (6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))*(19+(10*sqrt(5))))
SA:V of Truncated Icosidodecahedron = (6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/((Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3)*(19+(10*sqrt(5))))

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