Volume of Pentakis Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
V = (15/76)*(23+(11*sqrt(5)))*(((76/19)/(RA/V))^3)*((sqrt((413+(162*sqrt(5))))/(23+(11*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.
Surface to Volume Ratio of Pentakis Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Pentakis Dodecahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = (15/76)*(23+(11*sqrt(5)))*(((76/19)/(RA/V))^3)*((sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))^3) --> (15/76)*(23+(11*sqrt(5)))*(((76/19)/(0.2))^3)*((sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))^3)
Evaluating ... ...
V = 15044.2273155497
STEP 3: Convert Result to Output's Unit
15044.2273155497 Cubic Meter --> No Conversion Required
FINAL ANSWER
15044.2273155497 15044.23 Cubic Meter <-- Volume of Pentakis Dodecahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
Shweta Patil has created this Calculator and 2500+ more calculators!
Verified by Mona Gladys
St Joseph's College (SJC), Bengaluru
Mona Gladys has verified this Calculator and 1800+ 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 Surface to Volume Ratio Formula

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)
V = (15/76)*(23+(11*sqrt(5)))*(((76/19)/(RA/V))^3)*((sqrt((413+(162*sqrt(5))))/(23+(11*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 Surface to Volume Ratio?

Volume of Pentakis Dodecahedron given Surface to Volume Ratio calculator uses 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) to calculate the Volume of Pentakis Dodecahedron, Volume of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron. Volume of Pentakis Dodecahedron is denoted by V symbol.

How to calculate Volume of Pentakis Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Pentakis Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Pentakis Dodecahedron (RA/V) and hit the calculate button. Here is how the Volume of Pentakis Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 15044.23 = (15/76)*(23+(11*sqrt(5)))*(((76/19)/(0.2))^3)*((sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))^3).

FAQ

What is Volume of Pentakis Dodecahedron given Surface to Volume Ratio?
Volume of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron and is represented as V = (15/76)*(23+(11*sqrt(5)))*(((76/19)/(RA/V))^3)*((sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))^3) or 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). Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.
How to calculate Volume of Pentakis Dodecahedron given Surface to Volume Ratio?
Volume of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron is calculated using 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). To calculate Volume of Pentakis Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Pentakis Dodecahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio 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)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!