Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord Calculator

✖Pentagram Chord of Small Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Small Stellated Dodecahedron.ⓘ Pentagram Chord of Small Stellated Dodecahedron [l_c(Pentagram)]

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✖Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.ⓘ Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord [r_c]

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Formula

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Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord

Formula

`"r"_{"c"} = ((sqrt(50+22*sqrt(5)))/4)*("l"_{"c(Pentagram)"}/(2+sqrt(5)))`

Example

`"24.68698m"=((sqrt(50+22*sqrt(5)))/4)*("42m"/(2+sqrt(5)))`

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Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))
r_c = ((sqrt(50+22*sqrt(5)))/4)*(l_c(Pentagram)/(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

Circumradius of Small Stellated Dodecahedron - (Measured in Meter) - Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.
Pentagram Chord of Small Stellated Dodecahedron - (Measured in Meter) - Pentagram Chord of Small Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Small Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagram Chord of Small Stellated Dodecahedron: 42 Meter --> 42 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = ((sqrt(50+22*sqrt(5)))/4)*(l_c(Pentagram)/(2+sqrt(5))) --> ((sqrt(50+22*sqrt(5)))/4)*(42/(2+sqrt(5)))

Evaluating ... ...

r_c = 24.6869805962839

STEP 3: Convert Result to Output's Unit

24.6869805962839 Meter --> No Conversion Required

FINAL ANSWER

24.6869805962839 ≈ 24.68698 Meter <-- Circumradius of Small Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Small Stellated Dodecahedron » Circumsphere Radius of Small Stellated Dodecahedron » Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 7 Circumsphere Radius of Small Stellated Dodecahedron Calculators

Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))

Circumsphere Radius of Small Stellated Dodecahedron given Total Surface Area

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))

Circumsphere Radius of Small Stellated Dodecahedron given Pyramidal Height

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))

Circumsphere Radius of Small Stellated Dodecahedron given Volume

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))

Circumsphere Radius of Small Stellated Dodecahedron given Ridge Length

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))

Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))

Circumsphere Radius of Small Stellated Dodecahedron

Go Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*Edge Length of Small Stellated Dodecahedron

Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord Formula

Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))
r_c = ((sqrt(50+22*sqrt(5)))/4)*(l_c(Pentagram)/(2+sqrt(5)))

What is Small Stellated Dodecahedron?

The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.

How to Calculate Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord?

Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord calculator uses Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5))) to calculate the Circumradius of Small Stellated Dodecahedron, Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord formula is defined as the radius of the sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its pentagram chord. Circumradius of Small Stellated Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord using this online calculator? To use this online calculator for Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord, enter Pentagram Chord of Small Stellated Dodecahedron (l_c(Pentagram)) and hit the calculate button. Here is how the Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord calculation can be explained with given input values -> 24.68698 = ((sqrt(50+22*sqrt(5)))/4)*(42/(2+sqrt(5))).

FAQ

What is Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord?

Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord formula is defined as the radius of the sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its pentagram chord and is represented as r_c = ((sqrt(50+22*sqrt(5)))/4)*(l_c(Pentagram)/(2+sqrt(5))) or Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5))). Pentagram Chord of Small Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Small Stellated Dodecahedron.

How to calculate Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord?

Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord formula is defined as the radius of the sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its pentagram chord is calculated using Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5))). To calculate Circumsphere Radius of Small Stellated Dodecahedron given Pentagram Chord, you need Pentagram Chord of Small Stellated Dodecahedron (l_c(Pentagram)). With our tool, you need to enter the respective value for Pentagram Chord of Small Stellated 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 Circumradius of Small Stellated Dodecahedron?

In this formula, Circumradius of Small Stellated Dodecahedron uses Pentagram Chord of Small Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*Edge Length of Small Stellated Dodecahedron
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))
Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))

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