Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius Calculator

✖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.ⓘ Circumradius of Small Stellated Dodecahedron [r_c]

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✖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.ⓘ Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius [AV]

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Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Small Stellated Dodecahedron: 25 Meter --> 25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AV = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*r_c)) --> ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*25))

Evaluating ... ...

AV = 0.268328157299975

STEP 3: Convert Result to Output's Unit

0.268328157299975 1 per Meter --> No Conversion Required

FINAL ANSWER

0.268328157299975 ≈ 0.268328 1 per Meter <-- SA:V of Small Stellated Dodecahedron

(Calculation completed in 00.007 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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< Surface to Volume Ratio of Small Stellated Dodecahedron Calculators

Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height

LaTeX Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(25+10*sqrt(5)))/(5*Pyramidal Height of Small Stellated Dodecahedron))

Surface to Volume Ratio of Small Stellated Dodecahedron given Ridge Length

LaTeX Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((1+sqrt(5))/(2*Ridge Length of Small Stellated Dodecahedron))

Surface to Volume Ratio of Small Stellated Dodecahedron given Pentagram Chord

LaTeX Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/Pentagram Chord of Small Stellated Dodecahedron)

Surface to Volume Ratio of Small Stellated Dodecahedron

LaTeX Go SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*(1/Edge Length of Small Stellated Dodecahedron)

Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius Formula

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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 Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius?

Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius calculator uses SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*Circumradius of Small Stellated Dodecahedron)) to calculate the SA:V of Small Stellated Dodecahedron, Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius formula is defined as the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron, calculated using its circumradius. SA:V of Small Stellated Dodecahedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius, enter Circumradius of Small Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 0.268328 = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*25)).

FAQ

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

Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius formula is defined as the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron, calculated using its circumradius and is represented as AV = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*r_c)) or SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*Circumradius of Small Stellated Dodecahedron)). 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.

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

Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius formula is defined as the numerical ratio of the total surface area of a Small Stellated Dodecahedron to the volume of the Small Stellated Dodecahedron, calculated using its circumradius is calculated using SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(50+22*sqrt(5)))/(4*Circumradius of Small Stellated Dodecahedron)). To calculate Surface to Volume Ratio of Small Stellated Dodecahedron given Circumradius, you need Circumradius of Small Stellated Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumradius 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 SA:V of Small Stellated Dodecahedron?

In this formula, SA:V of Small Stellated Dodecahedron uses Circumradius of Small Stellated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*(1/Edge Length of Small Stellated Dodecahedron)
SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((1+sqrt(5))/(2*Ridge Length of Small Stellated Dodecahedron))
SA:V of Small Stellated Dodecahedron = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((2+sqrt(5))/Pentagram Chord of Small Stellated Dodecahedron)

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