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Volume of Great Stellated Dodecahedron given Pyramidal Height Formula

GoVolume of Great Stellated Dodecahedron Formula

GoVolume of Great Stellated Dodecahedron given Ridge Length Formula

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Volume of Great Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron. Check FAQs

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

V - Volume of Great Stellated Dodecahedron?h_Pyramid - Pyramidal Height of Great Stellated Dodecahedron?

Volume of Great Stellated Dodecahedron given Pyramidal Height Example

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

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

Here is how the Volume of Great Stellated Dodecahedron given Pyramidal Height equation looks like.

6396.5398 = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{6 \cdot 15}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

6396.5398m³ = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{6 \cdot 15m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

6396.5398 = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{6 \cdot 15}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

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Volume of Great Stellated Dodecahedron given Pyramidal Height Solution

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

FIRST Step Consider the formula

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{6 \cdot 15m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{6 \cdot 15}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

Next Step Evaluate

∴

V = 6396.53980674237m³

LAST Step Rounding Answer

∴

V = 6396.5398m³

Volume of Great Stellated Dodecahedron given Pyramidal Height Formula Elements

Variables

Functions

Volume of Great Stellated Dodecahedron

Volume of Great Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Great Stellated Dodecahedron

Pyramidal Height of Great Stellated Dodecahedron

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

Symbol: h_Pyramid

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Pyramidal Height of Great Stellated 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 Volume of Great Stellated Dodecahedron

Go Volume of Great Stellated Dodecahedron

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {l e}^{3}

Go Volume of Great Stellated Dodecahedron given Ridge Length

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot l Ridge}{1 + \sqrt{5}})}^{3}

Go Volume of Great Stellated Dodecahedron given Pentagram Chord

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{l c(Pentagram)}{2 + \sqrt{5}})}^{3}

Go Volume of Great Stellated Dodecahedron given Circumradius

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

How to Evaluate Volume of Great Stellated Dodecahedron given Pyramidal Height?

Volume of Great Stellated Dodecahedron given Pyramidal Height evaluator uses Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3 to evaluate the Volume of Great Stellated Dodecahedron, Volume of Great Stellated Dodecahedron given Pyramidal Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron, calculated using its pyramidal height. Volume of Great Stellated Dodecahedron is denoted by V symbol.

How to evaluate Volume of Great Stellated Dodecahedron given Pyramidal Height using this online evaluator? To use this online evaluator for Volume of Great Stellated Dodecahedron given Pyramidal Height, enter Pyramidal Height of Great Stellated Dodecahedron (h_Pyramid) and hit the calculate button.

FAQs on Volume of Great Stellated Dodecahedron given Pyramidal Height

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

The formula of Volume of Great Stellated Dodecahedron given Pyramidal Height is expressed as Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3. Here is an example- 6396.54 = 5/4*(3+sqrt(5))*((6*15)/(sqrt(3)*(3+sqrt(5))))^3.

How to calculate Volume of Great Stellated Dodecahedron given Pyramidal Height?

With Pyramidal Height of Great Stellated Dodecahedron (h_Pyramid) we can find Volume of Great Stellated Dodecahedron given Pyramidal Height using the formula - Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Great Stellated Dodecahedron?

Here are the different ways to Calculate Volume of Great Stellated Dodecahedron-

Volume of Great Stellated Dodecahedron=5/4*(3+sqrt(5))*Edge Length of Great Stellated Dodecahedron^3
Volume of Great Stellated Dodecahedron=5/4*(3+sqrt(5))*((2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5)))^3
Volume of Great Stellated Dodecahedron=5/4*(3+sqrt(5))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^3

Can the Volume of Great Stellated Dodecahedron given Pyramidal Height be negative?

No, the Volume of Great Stellated Dodecahedron given Pyramidal Height, measured in Volume cannot be negative.

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

Volume of Great Stellated Dodecahedron given Pyramidal Height is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Great Stellated Dodecahedron given Pyramidal Height can be measured.

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