Total Surface Area of Rhombicosidodecahedron given Midsphere Radius Calculator

✖Midsphere Radius of Rhombicosidodecahedron is the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Rhombicosidodecahedron [r_m]

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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 Midsphere Radius [TSA]

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Total Surface Area of Rhombicosidodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
TSA = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/(sqrt(10+(4*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.
Midsphere Radius of Rhombicosidodecahedron - (Measured in Meter) - Midsphere Radius of Rhombicosidodecahedron is the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Rhombicosidodecahedron: 21 Meter --> 21 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/(sqrt(10+(4*sqrt(5)))))^2 --> (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*21)/(sqrt(10+(4*sqrt(5)))))^2

Evaluating ... ...

TSA = 5522.28949391328

STEP 3: Convert Result to Output's Unit

5522.28949391328 Square Meter --> No Conversion Required

FINAL ANSWER

5522.28949391328 ≈ 5522.289 Square Meter <-- Total Surface Area of Rhombicosidodecahedron

(Calculation completed in 00.004 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 Midsphere Radius Formula

LaTeX Go

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 Midsphere Radius?

Total Surface Area of Rhombicosidodecahedron given Midsphere Radius calculator uses 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 to calculate the Total Surface Area of Rhombicosidodecahedron, Total Surface Area of Rhombicosidodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Rhombicosidodecahedron, and calculated using the midsphere radius of the Rhombicosidodecahedron. Total Surface Area of Rhombicosidodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Rhombicosidodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Rhombicosidodecahedron given Midsphere Radius, enter Midsphere Radius of Rhombicosidodecahedron (r_m) and hit the calculate button. Here is how the Total Surface Area of Rhombicosidodecahedron given Midsphere Radius calculation can be explained with given input values -> 5522.289 = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*21)/(sqrt(10+(4*sqrt(5)))))^2.

FAQ

What is Total Surface Area of Rhombicosidodecahedron given Midsphere Radius?

Total Surface Area of Rhombicosidodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Rhombicosidodecahedron, and calculated using the midsphere radius of the Rhombicosidodecahedron and is represented as TSA = (30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/(sqrt(10+(4*sqrt(5)))))^2 or 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. Midsphere Radius of Rhombicosidodecahedron is the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere.

How to calculate Total Surface Area of Rhombicosidodecahedron given Midsphere Radius?

Total Surface Area of Rhombicosidodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Rhombicosidodecahedron, and calculated using the midsphere radius of the Rhombicosidodecahedron is calculated using 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. To calculate Total Surface Area of Rhombicosidodecahedron given Midsphere Radius, you need Midsphere Radius of Rhombicosidodecahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius 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 Midsphere Radius 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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