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Volume of Pentakis Dodecahedron given Insphere Radius Formula

GoVolume of Pentakis Dodecahedron Formula

GoVolume of Pentakis Dodecahedron given Leg Length Formula

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

V = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{2 \cdot r i}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{3})

V - Volume of Pentakis Dodecahedron?r_i - Insphere Radius of Pentakis Dodecahedron?

Volume of Pentakis Dodecahedron given Insphere Radius Example

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

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

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

7702.6444 = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{2 \cdot 12}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{3})

7702.6444m³ = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{2 \cdot 12m}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{3})

7702.6444 = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{2 \cdot 12}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{3})

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Volume of Pentakis Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

V = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{2 \cdot r i}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{3})

Next Step Substitute values of Variables

∴

V = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{2 \cdot 12m}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{3})

Next Step Prepare to Evaluate

∴

V = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{2 \cdot 12}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{3})

Next Step Evaluate

∴

V = 7702.64438556147m³

LAST Step Rounding Answer

∴

V = 7702.6444m³

Volume of Pentakis Dodecahedron given Insphere Radius Formula Elements

Variables

Functions

Volume of Pentakis Dodecahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Pentakis Dodecahedron

Insphere Radius of Pentakis Dodecahedron

Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius of Pentakis 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 Pentakis Dodecahedron

Go Volume of Pentakis Dodecahedron

V = (\frac{15}{76}) \cdot ({l Base}^{3}) \cdot (23 + (11 \cdot \sqrt{5}))

Go Volume of Pentakis Dodecahedron given Leg Length

V = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{38 \cdot l Leg}{3 \cdot (9 + \sqrt{5})})}^{3})

Go Volume of Pentakis Dodecahedron given Total Surface Area

V = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{19 \cdot TSA}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})})}^{\frac{3}{2}})

Go Volume of Pentakis Dodecahedron given Midsphere Radius

V = (\frac{15}{76}) \cdot (23 + (11 \cdot \sqrt{5})) \cdot ({(\frac{4 \cdot r m}{3 + \sqrt{5}})}^{3})

How to Evaluate Volume of Pentakis Dodecahedron given Insphere Radius?

Volume of Pentakis Dodecahedron given Insphere Radius evaluator uses Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3) to evaluate the Volume of Pentakis Dodecahedron, Volume of Pentakis Dodecahedron given Insphere Radius formula is defined as quantity of three dimensional space covered by closed surface of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron. Volume of Pentakis Dodecahedron is denoted by V symbol.

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

FAQs on Volume of Pentakis Dodecahedron given Insphere Radius

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

The formula of Volume of Pentakis Dodecahedron given Insphere Radius is expressed as Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3). Here is an example- 7702.644 = (15/76)*(23+(11*sqrt(5)))*(((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3).

How to calculate Volume of Pentakis Dodecahedron given Insphere Radius?

With Insphere Radius of Pentakis Dodecahedron (r_i) we can find Volume of Pentakis Dodecahedron given Insphere Radius using the formula - Volume of Pentakis Dodecahedron = (15/76)*(23+(11*sqrt(5)))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^3). This formula also uses Square Root (sqrt) function(s).

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

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

Volume of Pentakis Dodecahedron=(15/76)*(Base Length of Pentakis Dodecahedron^3)*(23+(11*sqrt(5)))
Volume of Pentakis Dodecahedron=(15/76)*(23+(11*sqrt(5)))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^3)
Volume of Pentakis Dodecahedron=(15/76)*(23+(11*sqrt(5)))*(((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5))))))^(3/2))

Can the Volume of Pentakis Dodecahedron given Insphere Radius be negative?

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

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

Volume of Pentakis Dodecahedron given Insphere 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 Pentakis Dodecahedron given Insphere Radius can be measured.

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