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Volume of Dodecahedron given Face Diagonal Formula

GoVolume of Dodecahedron Formula

GoVolume of Dodecahedron given Space Diagonal Formula

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

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot d Face}{1 + \sqrt{5}})}^{3}

V - Volume of Dodecahedron?d_Face - Face Diagonal of Dodecahedron?

Volume of Dodecahedron given Face Diagonal Example

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Here is how the Volume of Dodecahedron given Face Diagonal equation looks like with Values.

Here is how the Volume of Dodecahedron given Face Diagonal equation looks like with Units.

Here is how the Volume of Dodecahedron given Face Diagonal equation looks like.

7409.7336 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{3}

7409.7336m³ = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{3}

7409.7336 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{3}

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Volume of Dodecahedron given Face Diagonal Solution

Follow our step by step solution on how to calculate Volume of Dodecahedron given Face Diagonal?

FIRST Step Consider the formula

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot d Face}{1 + \sqrt{5}})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{3}

Next Step Evaluate

∴

V = 7409.73360895978m³

LAST Step Rounding Answer

∴

V = 7409.7336m³

Volume of Dodecahedron given Face Diagonal Formula Elements

Variables

Functions

Volume of Dodecahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Dodecahedron

Face Diagonal of Dodecahedron

The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.

Symbol: d_Face

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Face Diagonal of 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 Dodecahedron

Go Volume of Dodecahedron

V = \frac{(15 + (7 \cdot \sqrt{5})) \cdot {l e}^{3}}{4}

Go Volume of Dodecahedron given Space Diagonal

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot d Space}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

Go Volume of Dodecahedron given Total Surface Area

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

Go Volume of Dodecahedron given Circumsphere Radius

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

How to Evaluate Volume of Dodecahedron given Face Diagonal?

Volume of Dodecahedron given Face Diagonal evaluator uses Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^3 to evaluate the Volume of Dodecahedron, The Volume of Dodecahedron given Face Diagonal formula is defined as the total quantity of three dimensional space enclosed by the surface of the Dodecahedron, and calculated using the face diagonal of Dodecahedron. Volume of Dodecahedron is denoted by V symbol.

How to evaluate Volume of Dodecahedron given Face Diagonal using this online evaluator? To use this online evaluator for Volume of Dodecahedron given Face Diagonal, enter Face Diagonal of Dodecahedron (d_Face) and hit the calculate button.

FAQs on Volume of Dodecahedron given Face Diagonal

What is the formula to find Volume of Dodecahedron given Face Diagonal?

The formula of Volume of Dodecahedron given Face Diagonal is expressed as Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^3. Here is an example- 7409.734 = 1/4*(15+(7*sqrt(5)))*((2*16)/(1+sqrt(5)))^3.

How to calculate Volume of Dodecahedron given Face Diagonal?

With Face Diagonal of Dodecahedron (d_Face) we can find Volume of Dodecahedron given Face Diagonal using the formula - Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^3. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Dodecahedron?

Here are the different ways to Calculate Volume of Dodecahedron-

Volume of Dodecahedron=((15+(7*sqrt(5)))*Edge Length of Dodecahedron^3)/4
Volume of Dodecahedron=1/4*(15+(7*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3
Volume of Dodecahedron=1/4*(15+(7*sqrt(5)))*(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))^(3/2)

Can the Volume of Dodecahedron given Face Diagonal be negative?

No, the Volume of Dodecahedron given Face Diagonal, measured in Volume cannot be negative.

Which unit is used to measure Volume of Dodecahedron given Face Diagonal?

Volume of Dodecahedron given Face Diagonal 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 Dodecahedron given Face Diagonal can be measured.

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