Circumsphere Radius of Small Stellated Dodecahedron Calculator

✖Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron.ⓘ Edge Length of Small Stellated Dodecahedron [l_e]

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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 [r_c]

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Circumsphere Radius of Small Stellated Dodecahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*Edge Length of Small Stellated Dodecahedron
r_c = ((sqrt(50+22*sqrt(5)))/4)*l_e
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.
Edge Length of Small Stellated Dodecahedron - (Measured in Meter) - Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Small Stellated Dodecahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = ((sqrt(50+22*sqrt(5)))/4)*l_e --> ((sqrt(50+22*sqrt(5)))/4)*10

Evaluating ... ...

r_c = 24.8989828488278

STEP 3: Convert Result to Output's Unit

24.8989828488278 Meter --> No Conversion Required

FINAL ANSWER

24.8989828488278 ≈ 24.89898 Meter <-- Circumradius of Small Stellated Dodecahedron

(Calculation completed in 00.020 seconds)

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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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< Circumsphere Radius of Small Stellated Dodecahedron Calculators

Circumsphere Radius of Small Stellated Dodecahedron given Pyramidal Height

LaTeX 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 Ridge Length

LaTeX 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

LaTeX 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

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

Circumsphere Radius of Small Stellated Dodecahedron Formula

LaTeX Go

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

What is Small Stellated Dodecahedron?

In geometry, 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?

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

How to calculate Circumsphere Radius of Small Stellated Dodecahedron using this online calculator? To use this online calculator for Circumsphere Radius of Small Stellated Dodecahedron, enter Edge Length of Small Stellated Dodecahedron (l_e) and hit the calculate button. Here is how the Circumsphere Radius of Small Stellated Dodecahedron calculation can be explained with given input values -> 24.89898 = ((sqrt(50+22*sqrt(5)))/4)*10.

FAQ

What is Circumsphere Radius of Small Stellated Dodecahedron?

Circumsphere Radius of Small Stellated Dodecahedron formula is defined as the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere and is represented as r_c = ((sqrt(50+22*sqrt(5)))/4)*l_e or Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*Edge Length of Small Stellated Dodecahedron. Edge Length of Small Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Small Stellated Dodecahedron.

How to calculate Circumsphere Radius of Small Stellated Dodecahedron?

Circumsphere Radius of Small Stellated Dodecahedron formula is defined as the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere is calculated using Circumradius of Small Stellated Dodecahedron = ((sqrt(50+22*sqrt(5)))/4)*Edge Length of Small Stellated Dodecahedron. To calculate Circumsphere Radius of Small Stellated Dodecahedron, you need Edge Length of Small Stellated Dodecahedron (l_e). With our tool, you need to enter the respective value for Edge Length 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 Edge Length of Small Stellated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)*(Pentagram Chord of Small Stellated Dodecahedron/(2+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))))

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