Credits

National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 1000+ more calculators!
Softusvista Office (Pune), India
Team Softusvista has verified this Calculator and 1000+ more calculators!

Volume of Regular Dodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = ((15+(7*sqrt(5)))*Side^3)/4
V = ((15+(7*sqrt(5)))*S^3)/4
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Side - The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Side: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = ((15+(7*sqrt(5)))*S^3)/4 --> ((15+(7*sqrt(5)))*9^3)/4
Evaluating ... ...
V = 5586.41372229536
STEP 3: Convert Result to Output's Unit
5586.41372229536 Cubic Meter --> No Conversion Required
FINAL ANSWER
5586.41372229536 Cubic Meter <-- Volume
(Calculation completed in 00.016 seconds)

10+ Volume Calculators

Volume of a Capsule
volume = pi*((Radius)^2)*((4/3)*Radius+Height) Go
Volume of a triangular prism
volume = (Length*Height*Base)/2 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 general pyramid
volume = (Base Area*Height)/3 Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Volume of a general prism
volume = Base Area*Height Go
Volume of a Cube
volume = Side^3 Go

6 Volume of Platonic Solids Calculators

Volume of Platonic Solids
volume_platonic = (1/24)*Length of edge^3*Number of edges in a face*Number of faces* cos((180*pi/180)/Number of edges meeting at a vertex)/(sin((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*cos((0.5*pi/180)*Dihedral Angle)) 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 Regular Tetrahedron
volume = (Side^3)/(6*sqrt(2)) Go
Volume of Regular Octahedron
volume = (sqrt(2))*(Side^3)/3 Go
Volume of a Cube
volume = Side^3 Go

Volume of Regular Dodecahedron Formula

volume = ((15+(7*sqrt(5)))*Side^3)/4
V = ((15+(7*sqrt(5)))*S^3)/4

How many sides are on a dodecahedron?

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. The octahedron can be divided into two pyramids. The volume of one pyramid = (base area × height) /3. In the case of the regular octahedron, the base area = a². And so, the volume of the octahedron = 2 × the volume of pyramid.

How to Calculate Volume of Regular Dodecahedron?

Volume of Regular Dodecahedron calculator uses volume = ((15+(7*sqrt(5)))*Side^3)/4 to calculate the Volume, Volume of Regular Dodecahedron, is the amount of the space which the shapes takes up. Volume and is denoted by V symbol.

How to calculate Volume of Regular Dodecahedron using this online calculator? To use this online calculator for Volume of Regular Dodecahedron, enter Side (S) and hit the calculate button. Here is how the Volume of Regular Dodecahedron calculation can be explained with given input values -> 5586.414 = ((15+(7*sqrt(5)))*9^3)/4.

FAQ

What is Volume of Regular Dodecahedron?
Volume of Regular Dodecahedron, is the amount of the space which the shapes takes up and is represented as V = ((15+(7*sqrt(5)))*S^3)/4 or volume = ((15+(7*sqrt(5)))*Side^3)/4. The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.
How to calculate Volume of Regular Dodecahedron?
Volume of Regular Dodecahedron, is the amount of the space which the shapes takes up is calculated using volume = ((15+(7*sqrt(5)))*Side^3)/4. To calculate Volume of Regular Dodecahedron, you need Side (S). With our tool, you need to enter the respective value for Side 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 Side. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • volume_platonic = (1/24)*Length of edge^3*Number of edges in a face*Number of faces* cos((180*pi/180)/Number of edges meeting at a vertex)/(sin((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*cos((0.5*pi/180)*Dihedral Angle))
  • volume = Side^3
  • volume = ((15+(7*sqrt(5)))*Side^3)/4
  • volume = (5*(3+sqrt(5))*Side^3)/12
  • volume = (sqrt(2))*(Side^3)/3
  • volume = (Side^3)/(6*sqrt(2))
Where is the Volume of Regular Dodecahedron calculator used?
Among many, Volume of Regular Dodecahedron calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
Share Image
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!