Credits

Walchand College of Engineering (WCE), Sangli
Shweta Patil has created this Calculator and 1000+ more calculators!
Indian Institute of Information Technology (IIIT), Bhopal
Mridul Sharma has verified this Calculator and 1000+ more calculators!

Volume (V) of Great Dodecahedron given Surface area (A) Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = ((5/4)*(sqrt(5)-1))*((sqrt(Area/(15*(sqrt(5-2*sqrt(5))))))^3)
V = ((5/4)*(sqrt(5)-1))*((sqrt(A/(15*(sqrt(5-2*sqrt(5))))))^3)
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Area - The area is the amount of two-dimensional space taken up by an object. (Measured in Square Meter)
STEP 1: Convert Input(s) to Base Unit
Area: 50 Square Meter --> 50 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = ((5/4)*(sqrt(5)-1))*((sqrt(A/(15*(sqrt(5-2*sqrt(5))))))^3) --> ((5/4)*(sqrt(5)-1))*((sqrt(50/(15*(sqrt(5-2*sqrt(5))))))^3)
Evaluating ... ...
V = 15.1837458319463
STEP 3: Convert Result to Output's Unit
15.1837458319463 Cubic Meter --> No Conversion Required
FINAL ANSWER
15.1837458319463 Cubic Meter <-- Volume
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Diagonal of a Rectangle when breadth and area are given
diagonal = sqrt(((Area)^2/(Breadth)^2)+(Breadth)^2) Go
Diagonal of a Rectangle when length and area are given
diagonal = sqrt(((Area)^2/(Length)^2)+(Length)^2) Go
Side of a Kite when other side and area are given
side_a = (Area*cosec(Angle Between Sides))/Side B Go
Perimeter of rectangle when area and rectangle length are given
perimeter = (2*Area+2*(Length)^2)/Length Go
Buoyant Force
buoyant_force = Pressure*Area Go
Perimeter of a square when area is given
perimeter = 4*sqrt(Area) Go
Diagonal of a Square when area is given
diagonal = sqrt(2*Area) Go
Length of rectangle when area and breadth are given
length = Area/Breadth Go
Breadth of rectangle when area and length are given
breadth = Area/Length Go
Pressure when force and area are given
pressure = Force/Area Go
Stress
stress = Force/Area Go

11 Other formulas that calculate the same Output

Volume of a Conical Frustum
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go
Volume of a Capsule
volume = pi*(Radius)^2*((4/3)*Radius+Side) Go
Volume of a Circular Cone
volume = (1/3)*pi*(Radius)^2*Height Go
Volume of a Circular Cylinder
volume = pi*(Radius)^2*Height Go
Volume of a Rectangular Prism
volume = Width*Height*Length Go
Volume of Regular Dodecahedron
volume = ((15+(7*sqrt(5)))*Side^3)/4 Go
Volume of Regular Icosahedron
volume = (5*(3+sqrt(5))*Side^3)/12 Go
Volume of a Hemisphere
volume = (2/3)*pi*(Radius)^3 Go
Volume of a Sphere
volume = (4/3)*pi*(Radius)^3 Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Volume of a Cube
volume = Side^3 Go

Volume (V) of Great Dodecahedron given Surface area (A) Formula

volume = ((5/4)*(sqrt(5)-1))*((sqrt(Area/(15*(sqrt(5-2*sqrt(5))))))^3)
V = ((5/4)*(sqrt(5)-1))*((sqrt(A/(15*(sqrt(5-2*sqrt(5))))))^3)

What is Great Dodecahedron?

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5,5/2} and Coxeter–Dynkin diagram of. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Volume (V) of Great Dodecahedron given Surface area (A)?

Volume (V) of Great Dodecahedron given Surface area (A) calculator uses volume = ((5/4)*(sqrt(5)-1))*((sqrt(Area/(15*(sqrt(5-2*sqrt(5))))))^3) to calculate the Volume, The Volume (V) of Great Dodecahedron given Surface area (A) formula is defined as amount of three dimensional space covered by Great Dodecahedron. Volume and is denoted by V symbol.

How to calculate Volume (V) of Great Dodecahedron given Surface area (A) using this online calculator? To use this online calculator for Volume (V) of Great Dodecahedron given Surface area (A), enter Area (A) and hit the calculate button. Here is how the Volume (V) of Great Dodecahedron given Surface area (A) calculation can be explained with given input values -> 15.18375 = ((5/4)*(sqrt(5)-1))*((sqrt(50/(15*(sqrt(5-2*sqrt(5))))))^3).

FAQ

What is Volume (V) of Great Dodecahedron given Surface area (A)?
The Volume (V) of Great Dodecahedron given Surface area (A) formula is defined as amount of three dimensional space covered by Great Dodecahedron and is represented as V = ((5/4)*(sqrt(5)-1))*((sqrt(A/(15*(sqrt(5-2*sqrt(5))))))^3) or volume = ((5/4)*(sqrt(5)-1))*((sqrt(Area/(15*(sqrt(5-2*sqrt(5))))))^3). The area is the amount of two-dimensional space taken up by an object.
How to calculate Volume (V) of Great Dodecahedron given Surface area (A)?
The Volume (V) of Great Dodecahedron given Surface area (A) formula is defined as amount of three dimensional space covered by Great Dodecahedron is calculated using volume = ((5/4)*(sqrt(5)-1))*((sqrt(Area/(15*(sqrt(5-2*sqrt(5))))))^3). To calculate Volume (V) of Great Dodecahedron given Surface area (A), you need Area (A). With our tool, you need to enter the respective value for Area 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?
In this formula, Volume uses Area. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • volume = pi*(Radius)^2*((4/3)*Radius+Side)
  • volume = (1/3)*pi*(Radius)^2*Height
  • volume = pi*(Radius)^2*Height
  • volume = Side^3
  • volume = (2/3)*pi*(Radius)^3
  • volume = (4/3)*pi*(Radius)^3
  • volume = (1/3)*Side^2*Height
  • volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2))
  • volume = Width*Height*Length
  • volume = ((15+(7*sqrt(5)))*Side^3)/4
  • volume = (5*(3+sqrt(5))*Side^3)/12
Share Image
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!