Volume of Rhombic Triacontahedron given Insphere Radius Calculator

✖Insphere Radius of Rhombic Triacontahedron is the radius of the sphere that is contained by the Rhombic Triacontahedron in such a way that all the faces are just touching the sphere.ⓘ Insphere Radius of Rhombic Triacontahedron [r_i]

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✖Volume of Rhombic Triacontahedron is the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron.ⓘ Volume of Rhombic Triacontahedron given Insphere Radius [V]

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Formula

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Volume of Rhombic Triacontahedron given Insphere Radius

Formula

`"V" = 4*("r"_{"i"}/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5)))`

Example

`"12955.41m³"=4*("14m"/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5)))`

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Volume of Rhombic Triacontahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Rhombic Triacontahedron = 4*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5)))
V = 4*(r_i/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5)))
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 Rhombic Triacontahedron - (Measured in Cubic Meter) - Volume of Rhombic Triacontahedron is the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron.
Insphere Radius of Rhombic Triacontahedron - (Measured in Meter) - Insphere Radius of Rhombic Triacontahedron is the radius of the sphere that is contained by the Rhombic Triacontahedron in such a way that all the faces are just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Rhombic Triacontahedron: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 4*(r_i/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5))) --> 4*(14/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5)))

Evaluating ... ...

V = 12955.4106051885

STEP 3: Convert Result to Output's Unit

12955.4106051885 Cubic Meter --> No Conversion Required

FINAL ANSWER

12955.4106051885 ≈ 12955.41 Cubic Meter <-- Volume of Rhombic Triacontahedron

(Calculation completed in 00.004 seconds)

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< 4 Volume of Rhombic Triacontahedron Calculators

Volume of Rhombic Triacontahedron given Insphere Radius

Go Volume of Rhombic Triacontahedron = 4*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5)))

Volume of Rhombic Triacontahedron given Total Surface Area

Go Volume of Rhombic Triacontahedron = 4*(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))^(3/2)*sqrt(5+(2*sqrt(5)))

Volume of Rhombic Triacontahedron given Midsphere Radius

Go Volume of Rhombic Triacontahedron = 4*((5*Midsphere Radius of Rhombic Triacontahedron)/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5)))

Volume of Rhombic Triacontahedron

Go Volume of Rhombic Triacontahedron = 4*Edge Length of Rhombic Triacontahedron^3*sqrt(5+(2*sqrt(5)))

Volume of Rhombic Triacontahedron given Insphere Radius Formula

Volume of Rhombic Triacontahedron = 4*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5)))
V = 4*(r_i/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5)))

What is Rhombic Triacontahedron?

In geometry, the Rhombic Triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron.

How to Calculate Volume of Rhombic Triacontahedron given Insphere Radius?

Volume of Rhombic Triacontahedron given Insphere Radius calculator uses Volume of Rhombic Triacontahedron = 4*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5))) to calculate the Volume of Rhombic Triacontahedron, Volume of Rhombic Triacontahedron given Insphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron, calculated using insphere radius of Rhombic Triancontahedron. Volume of Rhombic Triacontahedron is denoted by V symbol.

How to calculate Volume of Rhombic Triacontahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Rhombic Triacontahedron given Insphere Radius, enter Insphere Radius of Rhombic Triacontahedron (r_i) and hit the calculate button. Here is how the Volume of Rhombic Triacontahedron given Insphere Radius calculation can be explained with given input values -> 12955.41 = 4*(14/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5))).

FAQ

What is Volume of Rhombic Triacontahedron given Insphere Radius?

Volume of Rhombic Triacontahedron given Insphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron, calculated using insphere radius of Rhombic Triancontahedron and is represented as V = 4*(r_i/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5))) or Volume of Rhombic Triacontahedron = 4*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5))). Insphere Radius of Rhombic Triacontahedron is the radius of the sphere that is contained by the Rhombic Triacontahedron in such a way that all the faces are just touching the sphere.

How to calculate Volume of Rhombic Triacontahedron given Insphere Radius?

Volume of Rhombic Triacontahedron given Insphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron, calculated using insphere radius of Rhombic Triancontahedron is calculated using Volume of Rhombic Triacontahedron = 4*(Insphere Radius of Rhombic Triacontahedron/sqrt((5+(2*sqrt(5)))/5))^3*sqrt(5+(2*sqrt(5))). To calculate Volume of Rhombic Triacontahedron given Insphere Radius, you need Insphere Radius of Rhombic Triacontahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Rhombic Triacontahedron 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 Rhombic Triacontahedron?

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

Volume of Rhombic Triacontahedron = 4*Edge Length of Rhombic Triacontahedron^3*sqrt(5+(2*sqrt(5)))
Volume of Rhombic Triacontahedron = 4*(Total Surface Area of Rhombic Triacontahedron/(12*sqrt(5)))^(3/2)*sqrt(5+(2*sqrt(5)))
Volume of Rhombic Triacontahedron = 4*((5*Midsphere Radius of Rhombic Triacontahedron)/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5)))

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