Total Surface Area 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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✖Total Surface Area of Truncated Icosidodecahedron is the total quantity of plane enclosed by the entire surface of the Truncated Icosidodecahedron.ⓘ Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio [TSA]

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Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Total Surface Area of Truncated Icosidodecahedron - (Measured in Square Meter) - Total Surface Area of Truncated Icosidodecahedron is the total quantity of plane enclosed by the entire 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

TSA = 30*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(R_A/V*(19+(10*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))) --> 30*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(0.1*(19+(10*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))

Evaluating ... ...

TSA = 12379.9030237905

STEP 3: Convert Result to Output's Unit

12379.9030237905 Square Meter --> No Conversion Required

FINAL ANSWER

12379.9030237905 ≈ 12379.9 Square Meter <-- Total Surface Area of Truncated Icosidodecahedron

(Calculation completed in 00.008 seconds)

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Indian Institute of Information Technology (IIIT), Bhopal

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< Total Surface Area of Truncated Icosidodecahedron Calculators

Total Surface Area of Truncated Icosidodecahedron given Circumsphere Radius

LaTeX Go Total Surface Area of Truncated Icosidodecahedron = 30*((2*Circumsphere Radius of Truncated Icosidodecahedron)/(sqrt(31+(12*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))

Total Surface Area of Truncated Icosidodecahedron given Midsphere Radius

LaTeX Go Total Surface Area of Truncated Icosidodecahedron = 30*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))

Total Surface Area of Truncated Icosidodecahedron given Volume

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

Total Surface Area of Truncated Icosidodecahedron

LaTeX Go Total Surface Area of Truncated Icosidodecahedron = 30*Edge Length of Truncated Icosidodecahedron^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))

Total Surface Area 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 Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio?

Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio calculator uses Total Surface Area of Truncated Icosidodecahedron = 30*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))) to calculate the Total Surface Area of Truncated Icosidodecahedron, Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosidodecahedron, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron. Total Surface Area of Truncated Icosidodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Total Surface Area 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 Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 12379.9 = 30*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(0.1*(19+(10*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))).

FAQ

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

Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosidodecahedron, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron and is represented as TSA = 30*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(R_A/V*(19+(10*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))) or Total Surface Area of Truncated Icosidodecahedron = 30*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*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 Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio?

Total Surface Area of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosidodecahedron, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron is calculated using Total Surface Area of Truncated Icosidodecahedron = 30*((6*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))). To calculate Total Surface Area 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 Total Surface Area of Truncated Icosidodecahedron?

In this formula, Total Surface Area 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 -

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

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