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Volume of Dodecahedron given Space Diagonal Formula

GoVolume of Dodecahedron Formula

GoVolume of Dodecahedron given Total Surface Area 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 Space}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

V - Volume of Dodecahedron?d_Space - Space Diagonal of Dodecahedron?

Volume of Dodecahedron given Space Diagonal Example

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

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

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

7642.4896 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

7642.4896m³ = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 28m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

7642.4896 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

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Volume of Dodecahedron given Space Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 28m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

Next Step Evaluate

∴

V = 7642.48964040848m³

LAST Step Rounding Answer

∴

V = 7642.4896m³

Volume of Dodecahedron given Space 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

Space Diagonal of Dodecahedron

The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space 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 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}

Go Volume of Dodecahedron given Face Area

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

How to Evaluate Volume of Dodecahedron given Space Diagonal?

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

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

FAQs on Volume of Dodecahedron given Space Diagonal

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

The formula of Volume of Dodecahedron given Space Diagonal is expressed as Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3. Here is an example- 7642.49 = 1/4*(15+(7*sqrt(5)))*((2*28)/(sqrt(3)*(1+sqrt(5))))^3.

How to calculate Volume of Dodecahedron given Space Diagonal?

With Space Diagonal of Dodecahedron (d_Space) we can find Volume of Dodecahedron given Space Diagonal using the formula - Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(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)))*(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))^(3/2)
Volume of Dodecahedron=1/4*(15+(7*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3

Can the Volume of Dodecahedron given Space Diagonal be negative?

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

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

Volume of Dodecahedron given Space 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 Space Diagonal can be measured.

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