Midsphere Radius of Truncated Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))
rm = (5+(3*sqrt(5)))/4*sqrt(TSA/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))
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
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.
Total Surface Area of Truncated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Truncated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Truncated Dodecahedron: 10000 Square Meter --> 10000 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = (5+(3*sqrt(5)))/4*sqrt(TSA/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))) --> (5+(3*sqrt(5)))/4*sqrt(10000/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))
Evaluating ... ...
rm = 29.1265781915615
STEP 3: Convert Result to Output's Unit
29.1265781915615 Meter --> No Conversion Required
FINAL ANSWER
29.1265781915615 29.12658 Meter <-- Midsphere Radius of Truncated Dodecahedron
(Calculation completed in 00.004 seconds)

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6 Midsphere Radius of Truncated Dodecahedron Calculators

Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio
Go Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))
Midsphere Radius of Truncated Dodecahedron given Total Surface Area
Go Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))
Midsphere Radius of Truncated Dodecahedron given Circumsphere Radius
Go Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*Circumsphere Radius of Truncated Dodecahedron/(sqrt(74+(30*sqrt(5))))
Midsphere Radius of Truncated Dodecahedron given Volume
Go Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)
Midsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length
Go Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
Midsphere Radius of Truncated Dodecahedron
Go Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*Edge Length of Truncated Dodecahedron

Midsphere Radius of Truncated Dodecahedron given Total Surface Area Formula

Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))
rm = (5+(3*sqrt(5)))/4*sqrt(TSA/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))

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 Midsphere Radius of Truncated Dodecahedron given Total Surface Area?

Midsphere Radius of Truncated Dodecahedron given Total Surface Area calculator uses Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))) to calculate the Midsphere Radius of Truncated Dodecahedron, Midsphere Radius of Truncated Dodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Truncated Dodecahedron. Midsphere Radius of Truncated Dodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Truncated Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Midsphere Radius of Truncated Dodecahedron given Total Surface Area, enter Total Surface Area of Truncated Dodecahedron (TSA) and hit the calculate button. Here is how the Midsphere Radius of Truncated Dodecahedron given Total Surface Area calculation can be explained with given input values -> 29.12658 = (5+(3*sqrt(5)))/4*sqrt(10000/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))).

FAQ

What is Midsphere Radius of Truncated Dodecahedron given Total Surface Area?
Midsphere Radius of Truncated Dodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Truncated Dodecahedron and is represented as rm = (5+(3*sqrt(5)))/4*sqrt(TSA/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))) or Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))). Total Surface Area of Truncated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron.
How to calculate Midsphere Radius of Truncated Dodecahedron given Total Surface Area?
Midsphere Radius of Truncated Dodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Truncated Dodecahedron is calculated using Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))). To calculate Midsphere Radius of Truncated Dodecahedron given Total Surface Area, you need Total Surface Area of Truncated Dodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area 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 Midsphere Radius of Truncated Dodecahedron?
In this formula, Midsphere Radius of Truncated Dodecahedron uses Total Surface Area of Truncated Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
  • Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
  • Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)
  • Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*Circumsphere Radius of Truncated Dodecahedron/(sqrt(74+(30*sqrt(5))))
  • Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))
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