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Volume of Truncated Dodecahedron given Midsphere Radius Formula

GoVolume of Truncated Dodecahedron Formula

GoVolume of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot r m}{5 + (3 \cdot \sqrt{5})})}^{3}

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

Volume of Truncated Dodecahedron given Midsphere Radius Example

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

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

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

82703.6489 = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 29}{5 + (3 \cdot \sqrt{5})})}^{3}

82703.6489m³ = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 29m}{5 + (3 \cdot \sqrt{5})})}^{3}

82703.6489 = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 29}{5 + (3 \cdot \sqrt{5})})}^{3}

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Volume of Truncated Dodecahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot r m}{5 + (3 \cdot \sqrt{5})})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 29m}{5 + (3 \cdot \sqrt{5})})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 29}{5 + (3 \cdot \sqrt{5})})}^{3}

Next Step Evaluate

∴

V = 82703.6488988165m³

LAST Step Rounding Answer

∴

V = 82703.6489m³

Volume of Truncated Dodecahedron given Midsphere Radius Formula Elements

Variables

Functions

Volume of Truncated Dodecahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Truncated Dodecahedron

Midsphere Radius of Truncated Dodecahedron

Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated 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 Truncated 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 Truncated Dodecahedron

Go Volume of Truncated Dodecahedron

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {l e}^{3}

Go Volume of Truncated Dodecahedron given Dodecahedral Edge Length

V = \frac{99 + (47 \cdot \sqrt{5})}{12 \cdot \sqrt{5}} \cdot {l e(Dodecahedron)}^{3}

Go Volume of Truncated Dodecahedron given Total Surface Area

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\sqrt{\frac{TSA}{5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}})}^{3}

Go Volume of Truncated Dodecahedron given Circumsphere Radius

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot r c}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{3}

How to Evaluate Volume of Truncated Dodecahedron given Midsphere Radius?

Volume of Truncated Dodecahedron given Midsphere Radius evaluator uses Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^3 to evaluate the Volume of Truncated Dodecahedron, Volume of Truncated Dodecahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Dodecahedron, and calculated using the midsphere radius of the Truncated Dodecahedron. Volume of Truncated Dodecahedron is denoted by V symbol.

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

FAQs on Volume of Truncated Dodecahedron given Midsphere Radius

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

The formula of Volume of Truncated Dodecahedron given Midsphere Radius is expressed as Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^3. Here is an example- 82703.65 = 5/12*(99+(47*sqrt(5)))*((4*29)/(5+(3*sqrt(5))))^3.

How to calculate Volume of Truncated Dodecahedron given Midsphere Radius?

With Midsphere Radius of Truncated Dodecahedron (r_m) we can find Volume of Truncated Dodecahedron given Midsphere Radius using the formula - Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^3. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Truncated Dodecahedron?

Here are the different ways to Calculate Volume of Truncated Dodecahedron-

Volume of Truncated Dodecahedron=5/12*(99+(47*sqrt(5)))*Edge Length of Truncated Dodecahedron^3
Volume of Truncated Dodecahedron=(99+(47*sqrt(5)))/(12*sqrt(5))*Dodecahedral Edge Length of Truncated Dodecahedron^3
Volume of Truncated Dodecahedron=5/12*(99+(47*sqrt(5)))*(sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))))^3

Can the Volume of Truncated Dodecahedron given Midsphere Radius be negative?

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

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

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

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