## Volume of Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^3
V = 1/4*(15+(7*sqrt(5)))*((2*ri)/(sqrt((25+(11*sqrt(5)))/10)))^3
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Volume of Dodecahedron - (Measured in Cubic Meter) - Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron.
Insphere Radius of Dodecahedron - (Measured in Meter) - Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Dodecahedron: 11 Meter --> 11 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = 1/4*(15+(7*sqrt(5)))*((2*ri)/(sqrt((25+(11*sqrt(5)))/10)))^3 --> 1/4*(15+(7*sqrt(5)))*((2*11)/(sqrt((25+(11*sqrt(5)))/10)))^3
Evaluating ... ...
V = 7387.43735895414
STEP 3: Convert Result to Output's Unit
7387.43735895414 Cubic Meter --> No Conversion Required
7387.43735895414 7387.437 Cubic Meter <-- Volume of Dodecahedron
(Calculation completed in 00.003 seconds)
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## < 12 Volume of Dodecahedron Calculators

Volume of Dodecahedron given Surface to Volume Ratio
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((12*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^3
Volume of Dodecahedron given Lateral Surface Area
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))^(3/2)
Volume of Dodecahedron given Total Surface Area
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))^(3/2)
Volume of Dodecahedron given Insphere Radius
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^3
Volume of Dodecahedron given Circumsphere Radius
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3
Volume of Dodecahedron given Face Area
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))^(3/2)
Volume of Dodecahedron given Space Diagonal
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3
Volume of Dodecahedron given Midsphere Radius
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^3
Volume of Dodecahedron given Face Diagonal
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^3
Volume of Dodecahedron given Face Perimeter
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Face Perimeter of Dodecahedron/5)^3
Volume of Dodecahedron given Perimeter
Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Perimeter of Dodecahedron/30)^3
Volume of Dodecahedron
Volume of Dodecahedron = ((15+(7*sqrt(5)))*Edge Length of Dodecahedron^3)/4

## Volume of Dodecahedron given Insphere Radius Formula

Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^3
V = 1/4*(15+(7*sqrt(5)))*((2*ri)/(sqrt((25+(11*sqrt(5)))/10)))^3

## What is a Dodecahedron?

A Dodecahedron is a symmetric and closed three dimensional shape with 12 identical pentagonal faces. It is a Platonic solid, which has 12 faces, 20 vertices and 30 edges. At each vertex, three pentagonal faces meet and at each edge, two pentagonal faces meet. Out of all the five Platonic solids with identical edge length, Dodecahedron will have the highest value of volume and surface area.

## What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

## How to Calculate Volume of Dodecahedron given Insphere Radius?

Volume of Dodecahedron given Insphere Radius calculator uses Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^3 to calculate the Volume of Dodecahedron, The Volume of Dodecahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Dodecahedron, and calculated using the insphere radius of Dodecahedron. Volume of Dodecahedron is denoted by V symbol.

How to calculate Volume of Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Dodecahedron given Insphere Radius, enter Insphere Radius of Dodecahedron (ri) and hit the calculate button. Here is how the Volume of Dodecahedron given Insphere Radius calculation can be explained with given input values -> 7387.437 = 1/4*(15+(7*sqrt(5)))*((2*11)/(sqrt((25+(11*sqrt(5)))/10)))^3.

### FAQ

What is Volume of Dodecahedron given Insphere Radius?
The Volume of Dodecahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Dodecahedron, and calculated using the insphere radius of Dodecahedron and is represented as V = 1/4*(15+(7*sqrt(5)))*((2*ri)/(sqrt((25+(11*sqrt(5)))/10)))^3 or Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^3. Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.
How to calculate Volume of Dodecahedron given Insphere Radius?
The Volume of Dodecahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Dodecahedron, and calculated using the insphere radius of Dodecahedron is calculated using Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^3. To calculate Volume of Dodecahedron given Insphere Radius, you need Insphere Radius of Dodecahedron (ri). With our tool, you need to enter the respective value for Insphere Radius of 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 Dodecahedron?
In this formula, Volume of Dodecahedron uses Insphere Radius of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
• Volume of Dodecahedron = ((15+(7*sqrt(5)))*Edge Length of Dodecahedron^3)/4
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))^(3/2)
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))^(3/2)
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Face Perimeter of Dodecahedron/5)^3
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^3
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^3
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((12*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^3
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))^(3/2)
• Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Perimeter of Dodecahedron/30)^3 Let Others Know