Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio Calculator

✖SA:V of Small Stellated Dodecahedron is the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron.ⓘ SA:V of Small Stellated Dodecahedron [AV]

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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 Surface to Volume Ratio [r_c]

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Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
r_c = ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*AV))
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.
SA:V of Small Stellated Dodecahedron - (Measured in 1 per Meter) - SA:V of Small Stellated Dodecahedron is the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

SA:V of Small Stellated Dodecahedron: 0.3 1 per Meter --> 0.3 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*AV)) --> ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*0.3))

Evaluating ... ...

r_c = 22.3606797749979

STEP 3: Convert Result to Output's Unit

22.3606797749979 Meter --> No Conversion Required

FINAL ANSWER

22.3606797749979 ≈ 22.36068 Meter <-- Circumradius of Small Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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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 given Surface to Volume Ratio Formula

LaTeX Go

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 Surface to Volume Ratio?

Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio calculator uses 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)) to calculate the Circumradius of Small Stellated Dodecahedron, Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its surface to volume ratio. Circumradius of Small Stellated Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio, enter SA:V of Small Stellated Dodecahedron (AV) and hit the calculate button. Here is how the Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 22.36068 = ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*0.3)).

FAQ

What is Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio?

Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its surface to volume ratio and is represented as r_c = ((sqrt(50+22*sqrt(5)))/4)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*AV)) or 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)). SA:V of Small Stellated Dodecahedron is the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron.

How to calculate Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio?

Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its surface to volume ratio is calculated using 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)). To calculate Circumsphere Radius of Small Stellated Dodecahedron given Surface to Volume Ratio, you need SA:V of Small Stellated Dodecahedron (AV). With our tool, you need to enter the respective value for SA:V 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 SA:V 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)*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)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))

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