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Volume of Dodecahedron given Midsphere Radius 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 r m}{3 + \sqrt{5}})}^{3}

V - Volume of Dodecahedron?r_m - Midsphere Radius of Dodecahedron?

Volume of Dodecahedron given Midsphere Radius Example

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Here is how the Volume of Dodecahedron given Midsphere Radius equation looks like with Values.

Here is how the Volume of Dodecahedron given Midsphere Radius equation looks like with Units.

Here is how the Volume of Dodecahedron given Midsphere Radius equation looks like.

7505.8481 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{3}

7505.8481m³ = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 13m}{3 + \sqrt{5}})}^{3}

7505.8481 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{3}

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Volume of Dodecahedron given Midsphere Radius Solution

Follow our step by step solution on how to calculate Volume of Dodecahedron given Midsphere Radius?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 13m}{3 + \sqrt{5}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{3}

Next Step Evaluate

∴

V = 7505.84807940223m³

LAST Step Rounding Answer

∴

V = 7505.8481m³

Volume of Dodecahedron given Midsphere Radius 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

Midsphere Radius of Dodecahedron

The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere Radius 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 Midsphere Radius?

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

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

FAQs on Volume of Dodecahedron given Midsphere Radius

What is the formula to find Volume of Dodecahedron given Midsphere Radius?

The formula of Volume of Dodecahedron given Midsphere Radius is expressed as Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^3. Here is an example- 7505.848 = 1/4*(15+(7*sqrt(5)))*((4*13)/(3+sqrt(5)))^3.

How to calculate Volume of Dodecahedron given Midsphere Radius?

With Midsphere Radius of Dodecahedron (r_m) we can find Volume of Dodecahedron given Midsphere Radius using the formula - Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+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 Midsphere Radius be negative?

No, the Volume of Dodecahedron given Midsphere Radius, measured in Volume cannot be negative.

Which unit is used to measure Volume of Dodecahedron given Midsphere Radius?

Volume of Dodecahedron given Midsphere Radius 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 Midsphere Radius can be measured.

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