Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.ⓘ Surface to Volume Ratio of Great Dodecahedron [R_A/V]

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✖Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.ⓘ Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio [h_Pyramid]

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Formula

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Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio

Formula

`"h"_{"Pyramid"} = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*"R"_{"A/V"})`

Example

`"2.222112m"=(sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*"0.7m⁻¹")`

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Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron)
h_Pyramid = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V)
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 Great Dodecahedron - (Measured in Meter) - Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.
Surface to Volume Ratio of Great Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Great Dodecahedron: 0.7 1 per Meter --> 0.7 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_Pyramid = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V) --> (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*0.7)

Evaluating ... ...

h_Pyramid = 2.22211219844483

STEP 3: Convert Result to Output's Unit

2.22211219844483 Meter --> No Conversion Required

FINAL ANSWER

2.22211219844483 ≈ 2.222112 Meter <-- Pyramidal Height of Great 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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Indian Institute of Information Technology (IIIT), Bhopal

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< 6 Pyramidal Height of Great Dodecahedron Calculators

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio

Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron)

Pyramidal Height of Great Dodecahedron given Total Surface Area

Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))

Pyramidal Height of Great Dodecahedron given Circumsphere Radius

Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))

Pyramidal Height of Great Dodecahedron given Volume

Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3)

Pyramidal Height of Great Dodecahedron given Ridge Length

Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)

Pyramidal Height of Great Dodecahedron

Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*Edge Length of Great Dodecahedron

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio Formula

What is Great Dodecahedron?

The Great Dodecahedron is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio?

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio calculator uses Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron) to calculate the Pyramidal Height of Great Dodecahedron, Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron, calculated using its surface to volume ratio. Pyramidal Height of Great Dodecahedron is denoted by h_Pyramid symbol.

How to calculate Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Great Dodecahedron (R_A/V) and hit the calculate button. Here is how the Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 2.222112 = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*0.7).

FAQ

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

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron, calculated using its surface to volume ratio and is represented as h_Pyramid = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V) or Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron). Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.

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

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron, calculated using its surface to volume ratio is calculated using Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron). To calculate Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Great Dodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Great 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 Great Dodecahedron?

In this formula, Pyramidal Height of Great Dodecahedron uses Surface to Volume Ratio of Great Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*Edge Length of Great Dodecahedron
Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)
Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))
Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))
Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3)

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