Volume of Cuboctahedron given Midsphere Radius Calculator

✖Midsphere Radius of Cuboctahedron is the radius of the sphere which is tangent to every edge of the Cuboctahedron and also is present in between its insphere and the circumsphere.ⓘ Midsphere Radius of Cuboctahedron [r_m]

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✖Volume of Cuboctahedron is the amount of 3-dimensional space enclosed by the surface of the Cuboctahedron.ⓘ Volume of Cuboctahedron given Midsphere Radius [V]

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Formula

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Volume of Cuboctahedron given Midsphere Radius

Formula

`"V" = 5*sqrt(2)/3*(2/sqrt(3)*"r"_{"m"})^3`

Example

`"2645.449m³"=5*sqrt(2)/3*(2/sqrt(3)*"9m")^3`

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Volume of Cuboctahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Cuboctahedron = 5*sqrt(2)/3*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^3
V = 5*sqrt(2)/3*(2/sqrt(3)*r_m)^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 Cuboctahedron - (Measured in Cubic Meter) - Volume of Cuboctahedron is the amount of 3-dimensional space enclosed by the surface of the Cuboctahedron.
Midsphere Radius of Cuboctahedron - (Measured in Meter) - Midsphere Radius of Cuboctahedron is the radius of the sphere which is tangent to every edge of the Cuboctahedron and also is present in between its insphere and the circumsphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Cuboctahedron: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5*sqrt(2)/3*(2/sqrt(3)*r_m)^3 --> 5*sqrt(2)/3*(2/sqrt(3)*9)^3

Evaluating ... ...

V = 2645.44892220583

STEP 3: Convert Result to Output's Unit

2645.44892220583 Cubic Meter --> No Conversion Required

FINAL ANSWER

2645.44892220583 ≈ 2645.449 Cubic Meter <-- Volume of Cuboctahedron

(Calculation completed in 00.004 seconds)

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< 7 Volume of Cuboctahedron Calculators

Volume of Cuboctahedron given Surface to Volume Ratio

Go Volume of Cuboctahedron = 5*sqrt(2)/3*((18+(6*sqrt(3)))/(5*sqrt(2)*Surface to Volume Ratio of Cuboctahedron))^3

Volume of Cuboctahedron given Total Surface Area

Go Volume of Cuboctahedron = 5*sqrt(2)/3*(Total Surface Area of Cuboctahedron/(2*(3+sqrt(3))))^(3/2)

Volume of Cuboctahedron given Lateral Surface Area

Go Volume of Cuboctahedron = 5*sqrt(2)/3*(Lateral Surface Area of Cuboctahedron/((2*sqrt(3))+4))^(3/2)

Volume of Cuboctahedron given Midsphere Radius

Go Volume of Cuboctahedron = 5*sqrt(2)/3*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^3

Volume of Cuboctahedron given Circumsphere Radius

Go Volume of Cuboctahedron = 5*sqrt(2)/3*Circumsphere Radius of Cuboctahedron^3

Volume of Cuboctahedron given Perimeter

Go Volume of Cuboctahedron = 5*sqrt(2)/3*(Perimeter of Cuboctahedron/24)^3

Volume of Cuboctahedron

Go Volume of Cuboctahedron = 5*sqrt(2)/3*Edge Length of Cuboctahedron^3

Volume of Cuboctahedron given Midsphere Radius Formula

Volume of Cuboctahedron = 5*sqrt(2)/3*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^3
V = 5*sqrt(2)/3*(2/sqrt(3)*r_m)^3

What is a Cuboctahedron?

A Cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is the only radially equilateral convex polyhedron.

How to Calculate Volume of Cuboctahedron given Midsphere Radius?

Volume of Cuboctahedron given Midsphere Radius calculator uses Volume of Cuboctahedron = 5*sqrt(2)/3*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^3 to calculate the Volume of Cuboctahedron, The Volume of Cuboctahedron given Midsphere Radius formula is defined as the amount of three-dimensional space enclosed by the surface of the Cuboctahedron, calculated using the midsphere radius of Cuboctahedron. Volume of Cuboctahedron is denoted by V symbol.

How to calculate Volume of Cuboctahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Cuboctahedron given Midsphere Radius, enter Midsphere Radius of Cuboctahedron (r_m) and hit the calculate button. Here is how the Volume of Cuboctahedron given Midsphere Radius calculation can be explained with given input values -> 2645.449 = 5*sqrt(2)/3*(2/sqrt(3)*9)^3.

FAQ

What is Volume of Cuboctahedron given Midsphere Radius?

The Volume of Cuboctahedron given Midsphere Radius formula is defined as the amount of three-dimensional space enclosed by the surface of the Cuboctahedron, calculated using the midsphere radius of Cuboctahedron and is represented as V = 5*sqrt(2)/3*(2/sqrt(3)*r_m)^3 or Volume of Cuboctahedron = 5*sqrt(2)/3*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^3. Midsphere Radius of Cuboctahedron is the radius of the sphere which is tangent to every edge of the Cuboctahedron and also is present in between its insphere and the circumsphere.

How to calculate Volume of Cuboctahedron given Midsphere Radius?

The Volume of Cuboctahedron given Midsphere Radius formula is defined as the amount of three-dimensional space enclosed by the surface of the Cuboctahedron, calculated using the midsphere radius of Cuboctahedron is calculated using Volume of Cuboctahedron = 5*sqrt(2)/3*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^3. To calculate Volume of Cuboctahedron given Midsphere Radius, you need Midsphere Radius of Cuboctahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Cuboctahedron 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 Cuboctahedron?

In this formula, Volume of Cuboctahedron uses Midsphere Radius of Cuboctahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Volume of Cuboctahedron = 5*sqrt(2)/3*Edge Length of Cuboctahedron^3
Volume of Cuboctahedron = 5*sqrt(2)/3*Circumsphere Radius of Cuboctahedron^3
Volume of Cuboctahedron = 5*sqrt(2)/3*(Lateral Surface Area of Cuboctahedron/((2*sqrt(3))+4))^(3/2)
Volume of Cuboctahedron = 5*sqrt(2)/3*((18+(6*sqrt(3)))/(5*sqrt(2)*Surface to Volume Ratio of Cuboctahedron))^3
Volume of Cuboctahedron = 5*sqrt(2)/3*(Total Surface Area of Cuboctahedron/(2*(3+sqrt(3))))^(3/2)
Volume of Cuboctahedron = 5*sqrt(2)/3*(Perimeter of Cuboctahedron/24)^3

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