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Circumradius of Great Stellated Dodecahedron given surface area Solution

STEP 0: Pre-Calculation Summary
Formula Used
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*sqrt(5))))))
rc = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(SA/(15*(sqrt(5+2*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(3)*(3+sqrt(5)))/4)*(sqrt(SA/(15*(sqrt(5+2*sqrt(5)))))) --> ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(50/(15*(sqrt(5+2*sqrt(5))))))
Evaluating ... ...
rc = 2.35957238118648
STEP 3: Convert Result to Output's Unit
2.35957238118648 Meter --> No Conversion Required
FINAL ANSWER
2.35957238118648 Meter <-- Circumradius
(Calculation completed in 00.015 seconds)

7 Circumradius of Great Stellated Dodecahedron Calculators

Circumradius of Great Stellated Dodecahedron given surface to volume ratio
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(3+sqrt(5))*Surface to Volume Ratio)) Go
Circumradius of Great Stellated Dodecahedron given surface area
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*sqrt(5)))))) Go
Circumradius of Great Stellated Dodecahedron given pyramid height
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5)))) Go
Circumradius of Great Stellated Dodecahedron given volume
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(((4*Volume)/(5*(3+sqrt(5))))^(1/3)) Go
Circumradius of Great Stellated Dodecahedron given ridge length
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((2*Ridge Length 1)/(1+sqrt(5))) Go
Circumradius of Great Stellated Dodecahedron given pentagram chord
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(Chord Length/(2+sqrt(5))) Go
Circumradius of Great Stellated Dodecahedron given edge length
circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*Side A Go

Circumradius of Great Stellated Dodecahedron given surface area Formula

circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*sqrt(5))))))
rc = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(SA/(15*(sqrt(5+2*sqrt(5))))))

What is Great Stellated Dodecahedron?

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {​⁵⁄₂,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.

How to Calculate Circumradius of Great Stellated Dodecahedron given surface area?

Circumradius of Great Stellated Dodecahedron given surface area calculator uses circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*sqrt(5)))))) to calculate the Circumradius, Circumradius of Great Stellated Dodecahedron given surface area formula is defined as a straight line connecting circumcenter and any point on circumsphere of Great Stellated Dodecahedron. Circumradius and is denoted by rc symbol.

How to calculate Circumradius of Great Stellated Dodecahedron given surface area using this online calculator? To use this online calculator for Circumradius of Great Stellated Dodecahedron given surface area, enter Surface Area (SA) and hit the calculate button. Here is how the Circumradius of Great Stellated Dodecahedron given surface area calculation can be explained with given input values -> 2.359572 = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(50/(15*(sqrt(5+2*sqrt(5)))))).

FAQ

What is Circumradius of Great Stellated Dodecahedron given surface area?
Circumradius of Great Stellated Dodecahedron given surface area formula is defined as a straight line connecting circumcenter and any point on circumsphere of Great Stellated Dodecahedron and is represented as rc = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(SA/(15*(sqrt(5+2*sqrt(5)))))) or circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*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 Great Stellated Dodecahedron given surface area?
Circumradius of Great Stellated Dodecahedron given surface area formula is defined as a straight line connecting circumcenter and any point on circumsphere of Great Stellated Dodecahedron is calculated using circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*sqrt(5)))))). To calculate Circumradius of Great Stellated 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 7 other way(s) to calculate the same, which is/are as follows -
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*Side A
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((2*Ridge Length 1)/(1+sqrt(5)))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(Chord Length/(2+sqrt(5)))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((6*Height)/(sqrt(3)*(3+sqrt(5))))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(sqrt(Surface Area/(15*(sqrt(5+2*sqrt(5))))))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*(((4*Volume)/(5*(3+sqrt(5))))^(1/3))
  • circumradius = ((sqrt(3)*(3+sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(3+sqrt(5))*Surface to Volume Ratio))
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