Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height Calculator

✖Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron.ⓘ Pyramidal Height of Small Stellated Dodecahedron [h_Pyramid]

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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 Pyramidal Height [AV]

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Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height 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(25+10*sqrt(5)))/(5*Pyramidal Height of Small Stellated Dodecahedron))
AV = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(25+10*sqrt(5)))/(5*h_Pyramid))
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.
Pyramidal Height of Small Stellated Dodecahedron - (Measured in Meter) - Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pyramidal Height of Small Stellated Dodecahedron: 14 Meter --> 14 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(25+10*sqrt(5)))/(5*h_Pyramid)) --> ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(25+10*sqrt(5)))/(5*14))

Evaluating ... ...

AV = 0.264871709464241

STEP 3: Convert Result to Output's Unit

0.264871709464241 1 per Meter --> No Conversion Required

FINAL ANSWER

0.264871709464241 ≈ 0.264872 1 per Meter <-- SA:V of Small Stellated Dodecahedron

(Calculation completed in 00.007 seconds)

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Walchand College of Engineering (WCE), Sangli

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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 Pyramidal Height 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 Pyramidal Height?

Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height calculator uses 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)) to calculate the SA:V of Small Stellated Dodecahedron, Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height 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 pyramidal height. SA:V of Small Stellated Dodecahedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height using this online calculator? To use this online calculator for Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height, enter Pyramidal Height of Small Stellated Dodecahedron (h_Pyramid) and hit the calculate button. Here is how the Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height calculation can be explained with given input values -> 0.264872 = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(25+10*sqrt(5)))/(5*14)).

FAQ

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

Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height 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 pyramidal height and is represented as AV = ((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))))*((sqrt(25+10*sqrt(5)))/(5*h_Pyramid)) or 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)). Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron.

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

Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height 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 pyramidal height is calculated using 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)). To calculate Surface to Volume Ratio of Small Stellated Dodecahedron given Pyramidal Height, you need Pyramidal Height of Small Stellated Dodecahedron (h_Pyramid). With our tool, you need to enter the respective value for Pyramidal Height 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 Pyramidal Height 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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