Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio Calculator

✖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 [R_A/V]

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

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Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Rhombicosidodecahedron*(60+(29*sqrt(5)))))^2
TSA = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(R_A/V*(60+(29*sqrt(5)))))^2
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 Rhombicosidodecahedron - (Measured in Square Meter) - Total Surface Area of Rhombicosidodecahedron is the total quantity of plane enclosed by the entire surface of the of the Rhombicosidodecahedron.
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.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Rhombicosidodecahedron: 0.1 1 per Meter --> 0.1 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(R_A/V*(60+(29*sqrt(5)))))^2 --> (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(0.1*(60+(29*sqrt(5)))))^2

Evaluating ... ...

TSA = 12044.5052970447

STEP 3: Convert Result to Output's Unit

12044.5052970447 Square Meter --> No Conversion Required

FINAL ANSWER

12044.5052970447 ≈ 12044.51 Square Meter <-- Total Surface Area of Rhombicosidodecahedron

(Calculation completed in 00.020 seconds)

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< Total Surface Area of Rhombicosidodecahedron Calculators

Total Surface Area of Rhombicosidodecahedron given Circumsphere Radius

LaTeX Go Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Circumsphere Radius of Rhombicosidodecahedron)/(sqrt(11+(4*sqrt(5)))))^2

Total Surface Area of Rhombicosidodecahedron given Midsphere Radius

LaTeX Go Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Rhombicosidodecahedron)/(sqrt(10+(4*sqrt(5)))))^2

Total Surface Area of Rhombicosidodecahedron given Volume

LaTeX Go Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*Volume of Rhombicosidodecahedron)/(60+(29*sqrt(5))))^(2/3)

Total Surface Area of Rhombicosidodecahedron

LaTeX Go Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Edge Length of Rhombicosidodecahedron^2

Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio 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 Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio?

Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio calculator uses Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Rhombicosidodecahedron*(60+(29*sqrt(5)))))^2 to calculate the Total Surface Area of Rhombicosidodecahedron, Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Rhombicosidodecahedron, and calculated using the surface to volume ratio of the Rhombicosidodecahedron. Total Surface Area of Rhombicosidodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Rhombicosidodecahedron (R_A/V) and hit the calculate button. Here is how the Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 12044.51 = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(0.1*(60+(29*sqrt(5)))))^2.

FAQ

What is Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio?

Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Rhombicosidodecahedron, and calculated using the surface to volume ratio of the Rhombicosidodecahedron and is represented as TSA = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(R_A/V*(60+(29*sqrt(5)))))^2 or Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Rhombicosidodecahedron*(60+(29*sqrt(5)))))^2. Surface to Volume Ratio of Rhombicosidodecahedron is the numerical ratio of the total surface area of a Rhombicosidodecahedron to the volume of the Rhombicosidodecahedron.

How to calculate Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio?

Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Rhombicosidodecahedron, and calculated using the surface to volume ratio of the Rhombicosidodecahedron is calculated using Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Rhombicosidodecahedron*(60+(29*sqrt(5)))))^2. To calculate Total Surface Area of Rhombicosidodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Rhombicosidodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Total Surface Area of Rhombicosidodecahedron?

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

Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Edge Length of Rhombicosidodecahedron^2
Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((3*Volume of Rhombicosidodecahedron)/(60+(29*sqrt(5))))^(2/3)
Total Surface Area of Rhombicosidodecahedron = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Circumsphere Radius of Rhombicosidodecahedron)/(sqrt(11+(4*sqrt(5)))))^2

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