Pyramidal Height 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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✖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 given Surface to Volume Ratio [h_Pyramid]

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Formula

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Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio

Formula

`"h"_{"Pyramid"} = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*"AV"))`

Example

`"12.36068m"=((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*"0.3m⁻¹"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

h_Pyramid = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*AV)) --> ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*0.3))

Evaluating ... ...

h_Pyramid = 12.3606797749979

STEP 3: Convert Result to Output's Unit

12.3606797749979 Meter --> No Conversion Required

FINAL ANSWER

12.3606797749979 ≈ 12.36068 Meter <-- Pyramidal Height of Small Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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< 7 Pyramidal Height of Small Stellated Dodecahedron Calculators

Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio

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

Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area

Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))

Pyramidal Height of Small Stellated Dodecahedron given Circumradius

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

Pyramidal Height of Small Stellated Dodecahedron given Volume

Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))

Pyramidal Height of Small Stellated Dodecahedron given Ridge Length

Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))

Pyramidal Height of Small Stellated Dodecahedron given Pentagram Chord

Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))

Pyramidal Height of Small Stellated Dodecahedron

Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron

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

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

Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio calculator uses Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron)) to calculate the Pyramidal Height of Small Stellated Dodecahedron, Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its surface to volume ratio. Pyramidal Height of Small Stellated Dodecahedron is denoted by h_Pyramid symbol.

How to calculate Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Pyramidal Height 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 Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 12.36068 = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*0.3)).

FAQ

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

Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its surface to volume ratio and is represented as h_Pyramid = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*AV)) or Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((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 Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio?

Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its surface to volume ratio is calculated using Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron)). To calculate Pyramidal Height 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 Pyramidal Height of Small Stellated Dodecahedron?

In this formula, Pyramidal Height of Small Stellated Dodecahedron uses SA:V of Small Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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