Volume 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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✖Volume of Rhombicosidodecahedron is the total quantity of three dimensional space enclosed by the surface of the Rhombicosidodecahedron.ⓘ Volume of Rhombicosidodecahedron given Midsphere Radius [V]

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Volume of Rhombicosidodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Rhombicosidodecahedron = (60+(29*sqrt(5)))/3*((2*Midsphere Radius of Rhombicosidodecahedron)/(sqrt(10+(4*sqrt(5)))))^3
V = (60+(29*sqrt(5)))/3*((2*r_m)/(sqrt(10+(4*sqrt(5)))))^3
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 Rhombicosidodecahedron - (Measured in Cubic Meter) - Volume of Rhombicosidodecahedron is the total quantity of three dimensional space enclosed by the surface 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

V = (60+(29*sqrt(5)))/3*((2*r_m)/(sqrt(10+(4*sqrt(5)))))^3 --> (60+(29*sqrt(5)))/3*((2*21)/(sqrt(10+(4*sqrt(5)))))^3

Evaluating ... ...

V = 37392.4801063871

STEP 3: Convert Result to Output's Unit

37392.4801063871 Cubic Meter --> No Conversion Required

FINAL ANSWER

37392.4801063871 ≈ 37392.48 Cubic Meter <-- Volume of Rhombicosidodecahedron

(Calculation completed in 00.005 seconds)

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< Volume of Rhombicosidodecahedron Calculators

Volume of Rhombicosidodecahedron given Total Surface Area

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

Volume of Rhombicosidodecahedron given Circumsphere Radius

LaTeX Go Volume of Rhombicosidodecahedron = (60+(29*sqrt(5)))/3*((2*Circumsphere Radius of Rhombicosidodecahedron)/(sqrt(11+(4*sqrt(5)))))^3

Volume of Rhombicosidodecahedron given Midsphere Radius

LaTeX Go Volume of Rhombicosidodecahedron = (60+(29*sqrt(5)))/3*((2*Midsphere Radius of Rhombicosidodecahedron)/(sqrt(10+(4*sqrt(5)))))^3

Volume of Rhombicosidodecahedron

LaTeX Go Volume of Rhombicosidodecahedron = (60+(29*sqrt(5)))/3*Edge Length of Rhombicosidodecahedron^3

Volume of Rhombicosidodecahedron given Midsphere Radius Formula

LaTeX Go

Volume of Rhombicosidodecahedron = (60+(29*sqrt(5)))/3*((2*Midsphere Radius of Rhombicosidodecahedron)/(sqrt(10+(4*sqrt(5)))))^3
V = (60+(29*sqrt(5)))/3*((2*r_m)/(sqrt(10+(4*sqrt(5)))))^3

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 Volume of Rhombicosidodecahedron given Midsphere Radius?

Volume of Rhombicosidodecahedron given Midsphere Radius calculator uses Volume of Rhombicosidodecahedron = (60+(29*sqrt(5)))/3*((2*Midsphere Radius of Rhombicosidodecahedron)/(sqrt(10+(4*sqrt(5)))))^3 to calculate the Volume of Rhombicosidodecahedron, Volume of Rhombicosidodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombicosidodecahedron, and calculated using the midsphere radius of the Rhombicosidodecahedron. Volume of Rhombicosidodecahedron is denoted by V symbol.

How to calculate Volume of Rhombicosidodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Rhombicosidodecahedron given Midsphere Radius, enter Midsphere Radius of Rhombicosidodecahedron (r_m) and hit the calculate button. Here is how the Volume of Rhombicosidodecahedron given Midsphere Radius calculation can be explained with given input values -> 37392.48 = (60+(29*sqrt(5)))/3*((2*21)/(sqrt(10+(4*sqrt(5)))))^3.

FAQ

What is Volume of Rhombicosidodecahedron given Midsphere Radius?

Volume of Rhombicosidodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombicosidodecahedron, and calculated using the midsphere radius of the Rhombicosidodecahedron and is represented as V = (60+(29*sqrt(5)))/3*((2*r_m)/(sqrt(10+(4*sqrt(5)))))^3 or Volume of Rhombicosidodecahedron = (60+(29*sqrt(5)))/3*((2*Midsphere Radius of Rhombicosidodecahedron)/(sqrt(10+(4*sqrt(5)))))^3. 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 Volume of Rhombicosidodecahedron given Midsphere Radius?

Volume of Rhombicosidodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombicosidodecahedron, and calculated using the midsphere radius of the Rhombicosidodecahedron is calculated using Volume of Rhombicosidodecahedron = (60+(29*sqrt(5)))/3*((2*Midsphere Radius of Rhombicosidodecahedron)/(sqrt(10+(4*sqrt(5)))))^3. To calculate Volume 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 Volume of Rhombicosidodecahedron?

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

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

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