Volume of Truncated Icosidodecahedron given Surface to Volume Ratio Calculator

✖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.ⓘ SA:V of Truncated Icosidodecahedron [R_A/V]

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✖Volume of Truncated Icosidodecahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron.ⓘ Volume of Truncated Icosidodecahedron given Surface to Volume Ratio [V]

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Volume of Truncated Icosidodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Volume of Truncated Icosidodecahedron - (Measured in Cubic Meter) - Volume of Truncated Icosidodecahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron.
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.

STEP 1: Convert Input(s) to Base Unit

SA:V of Truncated Icosidodecahedron: 0.1 1 per Meter --> 0.1 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(R_A/V*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5))) --> 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(0.1*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5)))

Evaluating ... ...

V = 123799.030237905

STEP 3: Convert Result to Output's Unit

123799.030237905 Cubic Meter --> No Conversion Required

FINAL ANSWER

123799.030237905 ≈ 123799 Cubic Meter <-- Volume of Truncated Icosidodecahedron

(Calculation completed in 00.020 seconds)

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< Volume of Truncated Icosidodecahedron Calculators

Volume of Truncated Icosidodecahedron given Total Surface Area

LaTeX Go Volume of Truncated Icosidodecahedron = 5*(sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))^3)*(19+(10*sqrt(5)))

Volume of Truncated Icosidodecahedron given Circumsphere Radius

LaTeX Go Volume of Truncated Icosidodecahedron = 5*((2*Circumsphere Radius of Truncated Icosidodecahedron)/(sqrt(31+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))

Volume of Truncated Icosidodecahedron given Midsphere Radius

LaTeX Go Volume of Truncated Icosidodecahedron = 5*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))

Volume of Truncated Icosidodecahedron

LaTeX Go Volume of Truncated Icosidodecahedron = 5*Edge Length of Truncated Icosidodecahedron^3*(19+(10*sqrt(5)))

Volume of Truncated Icosidodecahedron given Surface to Volume Ratio Formula

LaTeX Go

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 Volume of Truncated Icosidodecahedron given Surface to Volume Ratio?

Volume of Truncated Icosidodecahedron given Surface to Volume Ratio calculator uses Volume of Truncated Icosidodecahedron = 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5))) to calculate the Volume of Truncated Icosidodecahedron, Volume of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron. Volume of Truncated Icosidodecahedron is denoted by V symbol.

How to calculate Volume of Truncated Icosidodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Truncated Icosidodecahedron given Surface to Volume Ratio, enter SA:V of Truncated Icosidodecahedron (R_A/V) and hit the calculate button. Here is how the Volume of Truncated Icosidodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 123799 = 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(0.1*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5))).

FAQ

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

Volume of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron and is represented as V = 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(R_A/V*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5))) or Volume of Truncated Icosidodecahedron = 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5))). 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.

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

Volume of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron is calculated using Volume of Truncated Icosidodecahedron = 5*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))))^3*(19+(10*sqrt(5))). To calculate Volume of Truncated Icosidodecahedron given Surface to Volume Ratio, you need SA:V of Truncated Icosidodecahedron (R_A/V). With our tool, you need to enter the respective value for SA:V 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 Volume of Truncated Icosidodecahedron?

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

Volume of Truncated Icosidodecahedron = 5*Edge Length of Truncated Icosidodecahedron^3*(19+(10*sqrt(5)))
Volume of Truncated Icosidodecahedron = 5*(sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))^3)*(19+(10*sqrt(5)))
Volume of Truncated Icosidodecahedron = 5*((2*Circumsphere Radius of Truncated Icosidodecahedron)/(sqrt(31+(12*sqrt(5)))))^3*(19+(10*sqrt(5)))

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