Volume of Icosidodecahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Icosidodecahedron [r_c]

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

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Formula

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Volume of Icosidodecahedron given Circumsphere Radius

Formula

`"V" = (45+(17*sqrt(5)))/6*((2*"r"_{"c"})/(1+sqrt(5)))^3`

Example

`"13378.05m³"=(45+(17*sqrt(5)))/6*((2*"16m")/(1+sqrt(5)))^3`

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Volume of Icosidodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5)))^3
V = (45+(17*sqrt(5)))/6*((2*r_c)/(1+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 Icosidodecahedron - (Measured in Cubic Meter) - Volume of Icosidodecahedron is the total quantity of three dimensional space enclosed by the surface of the Icosidodecahedron.
Circumsphere Radius of Icosidodecahedron - (Measured in Meter) - Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Icosidodecahedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (45+(17*sqrt(5)))/6*((2*r_c)/(1+sqrt(5)))^3 --> (45+(17*sqrt(5)))/6*((2*16)/(1+sqrt(5)))^3

Evaluating ... ...

V = 13378.0464657051

STEP 3: Convert Result to Output's Unit

13378.0464657051 Cubic Meter --> No Conversion Required

FINAL ANSWER

13378.0464657051 ≈ 13378.05 Cubic Meter <-- Volume of Icosidodecahedron

(Calculation completed in 00.004 seconds)

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< 5 Volume of Icosidodecahedron Calculators

Volume of Icosidodecahedron given Surface to Volume Ratio

Go Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Icosidodecahedron*(45+(17*sqrt(5)))))^3

Volume of Icosidodecahedron given Total Surface Area

Go Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*(sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))))^3

Volume of Icosidodecahedron given Midsphere Radius

Go Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5)))))^3

Volume of Icosidodecahedron given Circumsphere Radius

Go Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5)))^3

Volume of Icosidodecahedron

Go Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*Edge Length of Icosidodecahedron^3

Volume of Icosidodecahedron given Circumsphere Radius Formula

Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5)))^3
V = (45+(17*sqrt(5)))/6*((2*r_c)/(1+sqrt(5)))^3

What is an Icosidodecahedron?

In geometry, an Icosidodecahedron is a closed and convex polyhedron with 20 (icosi) triangular faces and 12 (dodeca) pentagonal faces. An Icosidodecahedron has 30 identical vertices, with 2 triangles and 2 pentagons meeting at each. And 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

How to Calculate Volume of Icosidodecahedron given Circumsphere Radius?

Volume of Icosidodecahedron given Circumsphere Radius calculator uses Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5)))^3 to calculate the Volume of Icosidodecahedron, Volume of Icosidodecahedron given Circumsphere Radius is defined as the total quantity of three dimensional space enclosed by the surface of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron. Volume of Icosidodecahedron is denoted by V symbol.

How to calculate Volume of Icosidodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Volume of Icosidodecahedron given Circumsphere Radius, enter Circumsphere Radius of Icosidodecahedron (r_c) and hit the calculate button. Here is how the Volume of Icosidodecahedron given Circumsphere Radius calculation can be explained with given input values -> 13378.05 = (45+(17*sqrt(5)))/6*((2*16)/(1+sqrt(5)))^3.

FAQ

What is Volume of Icosidodecahedron given Circumsphere Radius?

Volume of Icosidodecahedron given Circumsphere Radius is defined as the total quantity of three dimensional space enclosed by the surface of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron and is represented as V = (45+(17*sqrt(5)))/6*((2*r_c)/(1+sqrt(5)))^3 or Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5)))^3. Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.

How to calculate Volume of Icosidodecahedron given Circumsphere Radius?

Volume of Icosidodecahedron given Circumsphere Radius is defined as the total quantity of three dimensional space enclosed by the surface of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron is calculated using Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5)))^3. To calculate Volume of Icosidodecahedron given Circumsphere Radius, you need Circumsphere Radius of Icosidodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of 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 Icosidodecahedron?

In this formula, Volume of Icosidodecahedron uses Circumsphere Radius of Icosidodecahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -

Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*Edge Length of Icosidodecahedron^3
Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*(sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))))^3
Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5)))))^3
Volume of Icosidodecahedron = (45+(17*sqrt(5)))/6*((6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Icosidodecahedron*(45+(17*sqrt(5)))))^3

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