Volume of Pentakis Dodecahedron given Insphere Radius Calculator

✖Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.ⓘ Insphere Radius of Pentakis Dodecahedron [r_i]

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

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Formula

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Volume of Pentakis Dodecahedron given Insphere Radius

Formula

`"V" = (15/76)*(23+(11*sqrt(5)))*(((2*"r"_{"i"})/(3*(sqrt((81+(35*sqrt(5)))/218))))^3)`

Example

`"7702.644m³"=(15/76)*(23+(11*sqrt(5)))*(((2*"12m")/(3*(sqrt((81+(35*sqrt(5)))/218))))^3)`

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Volume of Pentakis Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3)
V = (15/76)*(23+(11*sqrt(5)))*(((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218))))^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 Pentakis Dodecahedron - (Measured in Cubic Meter) - Volume of Pentakis Dodecahedron is the quantity of three dimensional space enclosed by the entire surface of Pentakis Dodecahedron.
Insphere Radius of Pentakis Dodecahedron - (Measured in Meter) - Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Pentakis Dodecahedron: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (15/76)*(23+(11*sqrt(5)))*(((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3) --> (15/76)*(23+(11*sqrt(5)))*(((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3)

Evaluating ... ...

V = 7702.64438556147

STEP 3: Convert Result to Output's Unit

7702.64438556147 Cubic Meter --> No Conversion Required

FINAL ANSWER

7702.64438556147 ≈ 7702.644 Cubic Meter <-- Volume of Pentakis Dodecahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 6 Volume of Pentakis Dodecahedron Calculators

Volume of Pentakis Dodecahedron given Surface to Volume Ratio

Go Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))^3)*((sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))^3)

Volume of Pentakis Dodecahedron given Total Surface Area

Go Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5))))))^(3/2))

Volume of Pentakis Dodecahedron given Insphere Radius

Go Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3)

Volume of Pentakis Dodecahedron given Midsphere Radius

Go Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^3)

Volume of Pentakis Dodecahedron given Leg Length

Go Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^3)

Volume of Pentakis Dodecahedron

Go Volume of Pentakis Dodecahedron = (15/76)*(Base Length of Pentakis Dodecahedron^3)*(23+(11*sqrt(5)))

Volume of Pentakis Dodecahedron given Insphere Radius Formula

What is Pentakis Dodecahedron?

A Pentakis Dodecahedron is a polyhedron with isosceles triangle faces. Five of these are attached as a pyramid on each face of a dodecahedron.
It has 60 faces, 90 edges, 32 vertices.

How to Calculate Volume of Pentakis Dodecahedron given Insphere Radius?

Volume of Pentakis Dodecahedron given Insphere Radius calculator uses Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3) to calculate the Volume of Pentakis Dodecahedron, Volume of Pentakis Dodecahedron given Insphere Radius formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron. Volume of Pentakis Dodecahedron is denoted by V symbol.

How to calculate Volume of Pentakis Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Pentakis Dodecahedron given Insphere Radius, enter Insphere Radius of Pentakis Dodecahedron (r_i) and hit the calculate button. Here is how the Volume of Pentakis Dodecahedron given Insphere Radius calculation can be explained with given input values -> 7702.644 = (15/76)*(23+(11*sqrt(5)))*(((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3).

FAQ

What is Volume of Pentakis Dodecahedron given Insphere Radius?

Volume of Pentakis Dodecahedron given Insphere Radius formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron and is represented as V = (15/76)*(23+(11*sqrt(5)))*(((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3) or Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3). Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.

How to calculate Volume of Pentakis Dodecahedron given Insphere Radius?

Volume of Pentakis Dodecahedron given Insphere Radius formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron is calculated using Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3). To calculate Volume of Pentakis Dodecahedron given Insphere Radius, you need Insphere Radius of Pentakis Dodecahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Pentakis Dodecahedron 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 Pentakis Dodecahedron?

In this formula, Volume of Pentakis Dodecahedron uses Insphere Radius of Pentakis Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Volume of Pentakis Dodecahedron = (15/76)*(Base Length of Pentakis Dodecahedron^3)*(23+(11*sqrt(5)))
Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^3)
Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5))))))^(3/2))
Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^3)
Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))^3)*((sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))^3)

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