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Circumradius of Truncated Dodecahedron given surface area Solution

STEP 0: Pre-Calculation Summary
Formula Used
circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5))))
rc = ((sqrt(SA/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5))))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Surface Area - The surface area of a three-dimensional shape is the sum of all of the surface areas of each of the sides. (Measured in Square Meter)
STEP 1: Convert Input(s) to Base Unit
Surface Area: 50 Square Meter --> 50 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = ((sqrt(SA/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5)))) --> ((sqrt(50/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5))))
Evaluating ... ...
rc = 1.44926586744162
STEP 3: Convert Result to Output's Unit
1.44926586744162 Meter --> No Conversion Required
FINAL ANSWER
1.44926586744162 Meter <-- Circumradius
(Calculation completed in 00.000 seconds)

6 Circumradius of Truncated Dodecahedron Calculators

Circumradius of Truncated Dodecahedron given surface to volume ratio
circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron given surface area
circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron given volume
circumradius = ((((12*Volume)/(5*(99+47*sqrt(5))))^(1/3))/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron given midradius
circumradius = (((4*Midradius)/(5+(3*sqrt(5))))/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron given edge length dodecahedron
circumradius = (((sqrt(5)*Edge length)/5)/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron
circumradius = (Side/4)*(sqrt(74+(30*sqrt(5)))) Go

Circumradius of Truncated Dodecahedron given surface area Formula

circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5))))
rc = ((sqrt(SA/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5))))

What is a truncated dodecahedron?

In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. 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 Circumradius of Truncated Dodecahedron given surface area?

Circumradius of Truncated Dodecahedron given surface area calculator uses circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5)))) to calculate the Circumradius, Circumradius of Truncated Dodecahedron given surface area formula is defined as a straight line connecting center and any point of circumsphere of truncated cuboctahedron ,Where side= truncated dodecahedron edge (a). Circumradius and is denoted by rc symbol.

How to calculate Circumradius of Truncated Dodecahedron given surface area using this online calculator? To use this online calculator for Circumradius of Truncated Dodecahedron given surface area, enter Surface Area (SA) and hit the calculate button. Here is how the Circumradius of Truncated Dodecahedron given surface area calculation can be explained with given input values -> 1.449266 = ((sqrt(50/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5)))).

FAQ

What is Circumradius of Truncated Dodecahedron given surface area?
Circumradius of Truncated Dodecahedron given surface area formula is defined as a straight line connecting center and any point of circumsphere of truncated cuboctahedron ,Where side= truncated dodecahedron edge (a) and is represented as rc = ((sqrt(SA/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5)))) or circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5)))). The surface area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.
How to calculate Circumradius of Truncated Dodecahedron given surface area?
Circumradius of Truncated Dodecahedron given surface area formula is defined as a straight line connecting center and any point of circumsphere of truncated cuboctahedron ,Where side= truncated dodecahedron edge (a) is calculated using circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5)))). To calculate Circumradius of Truncated Dodecahedron given surface area, you need Surface Area (SA). With our tool, you need to enter the respective value for Surface 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 Circumradius?
In this formula, Circumradius uses Surface Area. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • circumradius = (Side/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = (((sqrt(5)*Edge length)/5)/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = ((((12*Volume)/(5*(99+47*sqrt(5))))^(1/3))/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = (((4*Midradius)/(5+(3*sqrt(5))))/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5))))
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