Volume of Deltoidal Icositetrahedron given Insphere Radius Calculator

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

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

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Formula

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Volume of Deltoidal Icositetrahedron given Insphere Radius

Formula

`"V" = 2/7*sqrt(292+(206*sqrt(2)))*("r"_{"i"}/(sqrt((22+(15*sqrt(2)))/34)))^3`

Example

`"51280.24m³"=2/7*sqrt(292+(206*sqrt(2)))*("22m"/(sqrt((22+(15*sqrt(2)))/34)))^3`

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Volume of Deltoidal Icositetrahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(Insphere Radius of Deltoidal Icositetrahedron/(sqrt((22+(15*sqrt(2)))/34)))^3
V = 2/7*sqrt(292+(206*sqrt(2)))*(r_i/(sqrt((22+(15*sqrt(2)))/34)))^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 Deltoidal Icositetrahedron - (Measured in Cubic Meter) - Volume of Deltoidal Icositetrahedron is the quantity of three dimensional space enclosed by the entire surface of Deltoidal Icositetrahedron.
Insphere Radius of Deltoidal Icositetrahedron - (Measured in Meter) - Insphere Radius of Deltoidal Icositetrahedron is the radius of the sphere that is contained by the Deltoidal Icositetrahedron in such a way that all the faces just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Deltoidal Icositetrahedron: 22 Meter --> 22 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 2/7*sqrt(292+(206*sqrt(2)))*(r_i/(sqrt((22+(15*sqrt(2)))/34)))^3 --> 2/7*sqrt(292+(206*sqrt(2)))*(22/(sqrt((22+(15*sqrt(2)))/34)))^3

Evaluating ... ...

V = 51280.2448039932

STEP 3: Convert Result to Output's Unit

51280.2448039932 Cubic Meter --> No Conversion Required

FINAL ANSWER

51280.2448039932 ≈ 51280.24 Cubic Meter <-- Volume of Deltoidal Icositetrahedron

(Calculation completed in 00.004 seconds)

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< 8 Volume of Deltoidal Icositetrahedron Calculators

Volume of Deltoidal Icositetrahedron given Total Surface Area

Go Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(sqrt((7*Total Surface Area of Deltoidal Icositetrahedron)/(12*sqrt(61+(38*sqrt(2))))))^3

Volume of Deltoidal Icositetrahedron given Surface to Volume Ratio

Go Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(6/SA:V of Deltoidal Icositetrahedron*sqrt((61+(38*sqrt(2)))/(292+(206*sqrt(2)))))^3

Volume of Deltoidal Icositetrahedron given NonSymmetry Diagonal

Go Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*((2*NonSymmetry Diagonal of Deltoidal Icositetrahedron)/(sqrt(4+(2*sqrt(2)))))^3

Volume of Deltoidal Icositetrahedron given Symmetry Diagonal

Go Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*((7*Symmetry Diagonal of Deltoidal Icositetrahedron)/(sqrt(46+(15*sqrt(2)))))^3

Volume of Deltoidal Icositetrahedron given Insphere Radius

Go Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(Insphere Radius of Deltoidal Icositetrahedron/(sqrt((22+(15*sqrt(2)))/34)))^3

Volume of Deltoidal Icositetrahedron given Midsphere Radius

Go Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*((2*Midsphere Radius of Deltoidal Icositetrahedron)/(1+sqrt(2)))^3

Volume of Deltoidal Icositetrahedron given Short Edge

Go Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*((7*Short Edge of Deltoidal Icositetrahedron)/(4+sqrt(2)))^3

Volume of Deltoidal Icositetrahedron

Go Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*Long Edge of Deltoidal Icositetrahedron^3

Volume of Deltoidal Icositetrahedron given Insphere Radius Formula

What is Deltoidal Icositetrahedron?

A Deltoidal Icositetrahedron is a polyhedron with deltoid (kite) faces, those have three angles with 81.579° and one with 115.263°. It has eight vertices with three edges and eighteen vertices with four edges. In total, it has 24 faces, 48 edges, 26 vertices.

How to Calculate Volume of Deltoidal Icositetrahedron given Insphere Radius?

Volume of Deltoidal Icositetrahedron given Insphere Radius calculator uses Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(Insphere Radius of Deltoidal Icositetrahedron/(sqrt((22+(15*sqrt(2)))/34)))^3 to calculate the Volume of Deltoidal Icositetrahedron, Volume of Deltoidal Icositetrahedron given Insphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Deltoidal Icositetrahedron, calculated using insphere radius of Deltoidal Icositetrahedron. Volume of Deltoidal Icositetrahedron is denoted by V symbol.

How to calculate Volume of Deltoidal Icositetrahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Deltoidal Icositetrahedron given Insphere Radius, enter Insphere Radius of Deltoidal Icositetrahedron (r_i) and hit the calculate button. Here is how the Volume of Deltoidal Icositetrahedron given Insphere Radius calculation can be explained with given input values -> 51280.24 = 2/7*sqrt(292+(206*sqrt(2)))*(22/(sqrt((22+(15*sqrt(2)))/34)))^3.

FAQ

What is Volume of Deltoidal Icositetrahedron given Insphere Radius?

Volume of Deltoidal Icositetrahedron given Insphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Deltoidal Icositetrahedron, calculated using insphere radius of Deltoidal Icositetrahedron and is represented as V = 2/7*sqrt(292+(206*sqrt(2)))*(r_i/(sqrt((22+(15*sqrt(2)))/34)))^3 or Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(Insphere Radius of Deltoidal Icositetrahedron/(sqrt((22+(15*sqrt(2)))/34)))^3. Insphere Radius of Deltoidal Icositetrahedron is the radius of the sphere that is contained by the Deltoidal Icositetrahedron in such a way that all the faces just touching the sphere.

How to calculate Volume of Deltoidal Icositetrahedron given Insphere Radius?

Volume of Deltoidal Icositetrahedron given Insphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Deltoidal Icositetrahedron, calculated using insphere radius of Deltoidal Icositetrahedron is calculated using Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(Insphere Radius of Deltoidal Icositetrahedron/(sqrt((22+(15*sqrt(2)))/34)))^3. To calculate Volume of Deltoidal Icositetrahedron given Insphere Radius, you need Insphere Radius of Deltoidal Icositetrahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Deltoidal Icositetrahedron 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 Deltoidal Icositetrahedron?

In this formula, Volume of Deltoidal Icositetrahedron uses Insphere Radius of Deltoidal Icositetrahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*Long Edge of Deltoidal Icositetrahedron^3
Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*((7*Short Edge of Deltoidal Icositetrahedron)/(4+sqrt(2)))^3
Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*((7*Symmetry Diagonal of Deltoidal Icositetrahedron)/(sqrt(46+(15*sqrt(2)))))^3
Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*((2*NonSymmetry Diagonal of Deltoidal Icositetrahedron)/(sqrt(4+(2*sqrt(2)))))^3
Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(sqrt((7*Total Surface Area of Deltoidal Icositetrahedron)/(12*sqrt(61+(38*sqrt(2))))))^3
Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*((2*Midsphere Radius of Deltoidal Icositetrahedron)/(1+sqrt(2)))^3
Volume of Deltoidal Icositetrahedron = 2/7*sqrt(292+(206*sqrt(2)))*(6/SA:V of Deltoidal Icositetrahedron*sqrt((61+(38*sqrt(2)))/(292+(206*sqrt(2)))))^3

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