Volume of Rhombic Triacontahedron given Midsphere Radius Calculator

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

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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 Midsphere Radius [V]

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Formula

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Volume of Rhombic Triacontahedron given Midsphere Radius

Formula

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

Example

`"13707.55m³"=4*((5*"15m")/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5)))`

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Volume of Rhombic Triacontahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Rhombic Triacontahedron = 4*((5*Midsphere Radius of Rhombic Triacontahedron)/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5)))
V = 4*((5*r_m)/(5+sqrt(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.
Midsphere Radius of Rhombic Triacontahedron - (Measured in Meter) - Midsphere Radius of Rhombic Triacontahedron is the radius of the sphere for which all the edges of the Rhombic Triacontahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Rhombic Triacontahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 4*((5*r_m)/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5))) --> 4*((5*15)/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5)))

Evaluating ... ...

V = 13707.5496848257

STEP 3: Convert Result to Output's Unit

13707.5496848257 Cubic Meter --> No Conversion Required

FINAL ANSWER

13707.5496848257 ≈ 13707.55 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 Midsphere Radius Formula

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

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

How to calculate Volume of Rhombic Triacontahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Rhombic Triacontahedron given Midsphere Radius, enter Midsphere Radius of Rhombic Triacontahedron (r_m) and hit the calculate button. Here is how the Volume of Rhombic Triacontahedron given Midsphere Radius calculation can be explained with given input values -> 13707.55 = 4*((5*15)/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5))).

FAQ

What is Volume of Rhombic Triacontahedron given Midsphere Radius?

Volume of Rhombic Triacontahedron given Midsphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Rhombic Triacontahedron, calculated using midsphere radius of Rhombic Triacontahedron and is represented as V = 4*((5*r_m)/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5))) or Volume of Rhombic Triacontahedron = 4*((5*Midsphere Radius of Rhombic Triacontahedron)/(5+sqrt(5)))^3*sqrt(5+(2*sqrt(5))). Midsphere Radius of Rhombic Triacontahedron is the radius of the sphere for which all the edges of the Rhombic Triacontahedron become a tangent line on that sphere.

How to calculate Volume of Rhombic Triacontahedron given Midsphere Radius?

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

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