Volume of Truncated Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^3
V = 5/12*(99+(47*sqrt(5)))*((4*rm)/(5+(3*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 Truncated Dodecahedron - (Measured in Cubic Meter) - Volume of Truncated Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Dodecahedron.
Midsphere Radius of Truncated Dodecahedron - (Measured in Meter) - Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Truncated Dodecahedron: 29 Meter --> 29 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = 5/12*(99+(47*sqrt(5)))*((4*rm)/(5+(3*sqrt(5))))^3 --> 5/12*(99+(47*sqrt(5)))*((4*29)/(5+(3*sqrt(5))))^3
Evaluating ... ...
V = 82703.6488988165
STEP 3: Convert Result to Output's Unit
82703.6488988165 Cubic Meter --> No Conversion Required
FINAL ANSWER
82703.6488988165 82703.65 Cubic Meter <-- Volume of Truncated Dodecahedron
(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru
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Walchand College of Engineering (WCE), Sangli
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Volume of Truncated Dodecahedron Calculators

Volume of Truncated Dodecahedron given Total Surface Area
​ LaTeX ​ Go Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*(sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))))^3
Volume of Truncated Dodecahedron given Circumsphere Radius
​ LaTeX ​ Go Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^3
Volume of Truncated Dodecahedron given Dodecahedral Edge Length
​ LaTeX ​ Go Volume of Truncated Dodecahedron = (99+(47*sqrt(5)))/(12*sqrt(5))*Dodecahedral Edge Length of Truncated Dodecahedron^3
Volume of Truncated Dodecahedron
​ LaTeX ​ Go Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*Edge Length of Truncated Dodecahedron^3

Volume of Truncated Dodecahedron given Midsphere Radius Formula

​LaTeX ​Go
Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^3
V = 5/12*(99+(47*sqrt(5)))*((4*rm)/(5+(3*sqrt(5))))^3

What is a Truncated Dodecahedron?

In geometry, the Truncated Dodecahedron is an Archimedean solid. It has a total of 32 faces - 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Each vertex is identical in such a way that two decagonal faces and one triangular face join at each vertex. This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. The Truncated Dodecahedron has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: hexagonal and pentagonal.

How to Calculate Volume of Truncated Dodecahedron given Midsphere Radius?

Volume of Truncated Dodecahedron given Midsphere Radius calculator uses Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^3 to calculate the Volume of Truncated Dodecahedron, Volume of Truncated Dodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Dodecahedron, and calculated using the midsphere radius of the Truncated Dodecahedron. Volume of Truncated Dodecahedron is denoted by V symbol.

How to calculate Volume of Truncated Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Truncated Dodecahedron given Midsphere Radius, enter Midsphere Radius of Truncated Dodecahedron (rm) and hit the calculate button. Here is how the Volume of Truncated Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 82703.65 = 5/12*(99+(47*sqrt(5)))*((4*29)/(5+(3*sqrt(5))))^3.

FAQ

What is Volume of Truncated Dodecahedron given Midsphere Radius?
Volume of Truncated Dodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Dodecahedron, and calculated using the midsphere radius of the Truncated Dodecahedron and is represented as V = 5/12*(99+(47*sqrt(5)))*((4*rm)/(5+(3*sqrt(5))))^3 or Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^3. Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere.
How to calculate Volume of Truncated Dodecahedron given Midsphere Radius?
Volume of Truncated Dodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Dodecahedron, and calculated using the midsphere radius of the Truncated Dodecahedron is calculated using Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^3. To calculate Volume of Truncated Dodecahedron given Midsphere Radius, you need Midsphere Radius of Truncated Dodecahedron (rm). With our tool, you need to enter the respective value for Midsphere Radius of Truncated 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 Truncated Dodecahedron?
In this formula, Volume of Truncated Dodecahedron uses Midsphere Radius of Truncated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*Edge Length of Truncated Dodecahedron^3
  • Volume of Truncated Dodecahedron = (99+(47*sqrt(5)))/(12*sqrt(5))*Dodecahedral Edge Length of Truncated Dodecahedron^3
  • Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*(sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))))^3
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