Volume of Pentakis Dodecahedron given Leg Length Calculator

✖Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron.ⓘ Leg Length of Pentakis Dodecahedron [l_Leg]

+10%

-10%

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

⎘ Copy

👎

Formula

✖

Volume of Pentakis Dodecahedron given Leg Length

Formula

`"V" = (15/76)*(23+(11*sqrt(5)))*(((38*"l"_{"Leg"})/(3*(9+sqrt(5))))^3)`

Example

`"9811.297m³"=(15/76)*(23+(11*sqrt(5)))*(((38*"9m")/(3*(9+sqrt(5))))^3)`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF

Volume of Pentakis Dodecahedron given Leg Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^3)
V = (15/76)*(23+(11*sqrt(5)))*(((38*l_Leg)/(3*(9+sqrt(5))))^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.
Leg Length of Pentakis Dodecahedron - (Measured in Meter) - Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Leg Length of Pentakis Dodecahedron: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (15/76)*(23+(11*sqrt(5)))*(((38*l_Leg)/(3*(9+sqrt(5))))^3) --> (15/76)*(23+(11*sqrt(5)))*(((38*9)/(3*(9+sqrt(5))))^3)

Evaluating ... ...

V = 9811.29706804634

STEP 3: Convert Result to Output's Unit

9811.29706804634 Cubic Meter --> No Conversion Required

FINAL ANSWER

9811.29706804634 ≈ 9811.297 Cubic Meter <-- Volume of Pentakis Dodecahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » CatalanSolids » Pentakis Dodecahedron » Volume of Pentakis Dodecahedron » Volume of Pentakis Dodecahedron given Leg Length

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< 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 Leg Length Formula

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

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 Leg Length?

Volume of Pentakis Dodecahedron given Leg Length calculator uses Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^3) to calculate the Volume of Pentakis Dodecahedron, Volume of Pentakis Dodecahedron given Leg Length formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using leg length of Pentakis Dodecahedron. Volume of Pentakis Dodecahedron is denoted by V symbol.

How to calculate Volume of Pentakis Dodecahedron given Leg Length using this online calculator? To use this online calculator for Volume of Pentakis Dodecahedron given Leg Length, enter Leg Length of Pentakis Dodecahedron (l_Leg) and hit the calculate button. Here is how the Volume of Pentakis Dodecahedron given Leg Length calculation can be explained with given input values -> 9811.297 = (15/76)*(23+(11*sqrt(5)))*(((38*9)/(3*(9+sqrt(5))))^3).

FAQ

What is Volume of Pentakis Dodecahedron given Leg Length?

Volume of Pentakis Dodecahedron given Leg Length formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using leg length of Pentakis Dodecahedron and is represented as V = (15/76)*(23+(11*sqrt(5)))*(((38*l_Leg)/(3*(9+sqrt(5))))^3) or Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^3). Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron.

How to calculate Volume of Pentakis Dodecahedron given Leg Length?

Volume of Pentakis Dodecahedron given Leg Length formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using leg length of Pentakis Dodecahedron is calculated using Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^3). To calculate Volume of Pentakis Dodecahedron given Leg Length, you need Leg Length of Pentakis Dodecahedron (l_Leg). With our tool, you need to enter the respective value for Leg Length 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 Leg Length 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)))*(((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)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^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)

Home

FREE PDFs

🔍 Search