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Volume of Dodecahedron given Face Area 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{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

V - Volume of Dodecahedron?A_Face - Face Area of Dodecahedron?

Volume of Dodecahedron given Face Area Example

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

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

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

7861.2061 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

7861.2061m³ = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 175m²}{\sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

7861.2061 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

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Volume of Dodecahedron given Face Area Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 175m²}{\sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

Next Step Evaluate

∴

V = 7861.2060929223m³

LAST Step Rounding Answer

∴

V = 7861.2061m³

Volume of Dodecahedron given Face Area 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 Area of Dodecahedron

The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area 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 Area?

Volume of Dodecahedron given Face Area evaluator uses Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))^(3/2) to evaluate the Volume of Dodecahedron, The Volume of Dodecahedron given Face Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Dodecahedron, and calculated using the face area of Dodecahedron. Volume of Dodecahedron is denoted by V symbol.

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

FAQs on Volume of Dodecahedron given Face Area

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

The formula of Volume of Dodecahedron given Face Area is expressed as Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))^(3/2). Here is an example- 7861.206 = 1/4*(15+(7*sqrt(5)))*((4*175)/(sqrt(25+(10*sqrt(5)))))^(3/2).

How to calculate Volume of Dodecahedron given Face Area?

With Face Area of Dodecahedron (A_Face) we can find Volume of Dodecahedron given Face Area using the formula - Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))^(3/2). 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 Area be negative?

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

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

Volume of Dodecahedron given Face Area 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 Area can be measured.

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