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Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio Formula

GoPyramidal Height of Great Dodecahedron Formula

GoPyramidal Height of Great Dodecahedron given Ridge Length Formula

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Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron. Check FAQs

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot R A/V}

h_Pyramid - Pyramidal Height of Great Dodecahedron?R_A/V - Surface to Volume Ratio of Great Dodecahedron?

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio Example

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Here is how the Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio equation looks like with Values.

Here is how the Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio equation looks like with Units.

Here is how the Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio equation looks like.

2.2221 = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7}

2.2221m = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7m⁻¹}

2.2221 = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7}

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Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio Solution

Follow our step by step solution on how to calculate Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio?

FIRST Step Consider the formula

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot R A/V}

Next Step Substitute values of Variables

∴

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7m⁻¹}

Next Step Prepare to Evaluate

∴

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7}

Next Step Evaluate

∴

h Pyramid = 2.22211219844483m

LAST Step Rounding Answer

∴

h Pyramid = 2.2221m

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Pyramidal Height of Great Dodecahedron

Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

Symbol: h_Pyramid

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Pyramidal Height of Great Dodecahedron

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.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Great Dodecahedron

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.

Syntax: sqrt(Number)

Other Formulas to find Pyramidal Height of Great Dodecahedron

Go Pyramidal Height of Great Dodecahedron

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot l e

Go Pyramidal Height of Great Dodecahedron given Ridge Length

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{2 \cdot l Ridge}{\sqrt{5} - 1}

Go Pyramidal Height of Great Dodecahedron given Circumsphere Radius

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Go Pyramidal Height of Great Dodecahedron given Total Surface Area

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

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

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio evaluator 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 evaluate 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 evaluate Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio using this online evaluator? To use this online evaluator 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.

FAQs on Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio

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

The formula of Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio is expressed as 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). Here is an example- 2.222112 = (sqrt(3)*(3-sqrt(5)))/6*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*0.7).

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

With Surface to Volume Ratio of Great Dodecahedron (R_A/V) we can find Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio using the formula - 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). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Pyramidal Height of Great Dodecahedron?

Here are the different ways to Calculate Pyramidal Height of Great Dodecahedron-

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)))

Can the Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio be negative?

No, the Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio, measured in Length cannot be negative.

Which unit is used to measure Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio?

Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Pyramidal Height of Great Dodecahedron given Surface to Volume Ratio can be measured.

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