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Volume of Star Pyramid given Pentagonal Edge Length of Base Formula

GoVolume of Star Pyramid Formula

GoVolume of Star Pyramid given Edge Length of Base Formula

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Volume of Star Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid. Check FAQs

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(l e(Pentagon) \cdot {[phi]}^{2})}^{2}}{6} \cdot h

V - Volume of Star Pyramid?l_e(Pentagon) - Pentagonal Edge Length of Base of Star Pyramid?h - Height of Star Pyramid?[phi] - Golden ratio?

Volume of Star Pyramid given Pentagonal Edge Length of Base Example

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Here is how the Volume of Star Pyramid given Pentagonal Edge Length of Base equation looks like with Values.

Here is how the Volume of Star Pyramid given Pentagonal Edge Length of Base equation looks like with Units.

Here is how the Volume of Star Pyramid given Pentagonal Edge Length of Base equation looks like.

207.8564 = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(4 \cdot {1.618}^{2})}^{2}}{6} \cdot 7

207.8564m³ = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(4m \cdot {1.618}^{2})}^{2}}{6} \cdot 7m

207.8564 = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(4 \cdot {1.618}^{2})}^{2}}{6} \cdot 7

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Volume of Star Pyramid given Pentagonal Edge Length of Base Solution

Follow our step by step solution on how to calculate Volume of Star Pyramid given Pentagonal Edge Length of Base?

FIRST Step Consider the formula

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(l e(Pentagon) \cdot {[phi]}^{2})}^{2}}{6} \cdot h

Next Step Substitute values of Variables

∴

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(4m \cdot {[phi]}^{2})}^{2}}{6} \cdot 7m

Next Step Substitute values of Constants

∴

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(4m \cdot {1.618}^{2})}^{2}}{6} \cdot 7m

Next Step Prepare to Evaluate

∴

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(4 \cdot {1.618}^{2})}^{2}}{6} \cdot 7

Next Step Evaluate

∴

V = 207.8563880235m³

LAST Step Rounding Answer

∴

V = 207.8564m³

Volume of Star Pyramid given Pentagonal Edge Length of Base Formula Elements

Variables

Constants

Functions

Volume of Star Pyramid

Volume of Star Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Star Pyramid

Pentagonal Edge Length of Base of Star Pyramid

Pentagonal Edge Length of Base of Star Pyramid is the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed.

Symbol: l_e(Pentagon)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Pentagonal Edge Length of Base of Star Pyramid

Height of Star Pyramid

Height of Star Pyramid is the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Star Pyramid

Golden ratio

The Golden ratio occurs when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

Symbol: [phi]

Value: 1.61803398874989484820458683436563811

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 Star Pyramid

Go Volume of Star Pyramid

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{l c}^{2}}{6} \cdot h

Go Volume of Star Pyramid given Edge Length of Base

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{(l e(Base) \cdot [phi])}^{2}}{6} \cdot h

Go Volume of Star Pyramid given Lateral Edge Length

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{l c}^{2}}{6} \cdot \sqrt{{l e(Lateral)}^{2} - (\frac{{l c}^{2}}{100} \cdot (50 + (10 \cdot \sqrt{5})))}

Other formulas in Volume and Surface to Volume Ratio of Star Pyramid category

Go Surface to Volume Ratio of Star Pyramid

R A/V = \frac{(\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{l c}^{2}}{2}) + (10 \cdot \sqrt{(\frac{l e(Base) + l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Lateral) + l e(Ridge) - l e(Base)}{2}) \cdot (\frac{l e(Base) - l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Base) + l e(Lateral) - l e(Ridge)}{2})})}{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{l c}^{2}}{6} \cdot h}

How to Evaluate Volume of Star Pyramid given Pentagonal Edge Length of Base?

Volume of Star Pyramid given Pentagonal Edge Length of Base evaluator uses Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*((Pentagonal Edge Length of Base of Star Pyramid*[phi]^2)^2)/6*Height of Star Pyramid to evaluate the Volume of Star Pyramid, Volume of Star Pyramid given Pentagonal Edge Length of Base formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid and is calculated using the pentagonal edge length of base, and height of the Star Pyramid. Volume of Star Pyramid is denoted by V symbol.

How to evaluate Volume of Star Pyramid given Pentagonal Edge Length of Base using this online evaluator? To use this online evaluator for Volume of Star Pyramid given Pentagonal Edge Length of Base, enter Pentagonal Edge Length of Base of Star Pyramid (l_e(Pentagon)) & Height of Star Pyramid (h) and hit the calculate button.

FAQs on Volume of Star Pyramid given Pentagonal Edge Length of Base

What is the formula to find Volume of Star Pyramid given Pentagonal Edge Length of Base?

The formula of Volume of Star Pyramid given Pentagonal Edge Length of Base is expressed as Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*((Pentagonal Edge Length of Base of Star Pyramid*[phi]^2)^2)/6*Height of Star Pyramid. Here is an example- 207.8564 = sqrt(5*(5-(2*sqrt(5))))*((4*[phi]^2)^2)/6*7.

How to calculate Volume of Star Pyramid given Pentagonal Edge Length of Base?

With Pentagonal Edge Length of Base of Star Pyramid (l_e(Pentagon)) & Height of Star Pyramid (h) we can find Volume of Star Pyramid given Pentagonal Edge Length of Base using the formula - Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*((Pentagonal Edge Length of Base of Star Pyramid*[phi]^2)^2)/6*Height of Star Pyramid. This formula also uses Golden ratio constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Star Pyramid?

Here are the different ways to Calculate Volume of Star Pyramid-

Volume of Star Pyramid=sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*Height of Star Pyramid
Volume of Star Pyramid=sqrt(5*(5-(2*sqrt(5))))*((Edge Length of Base of Star Pyramid*[phi])^2)/6*Height of Star Pyramid
Volume of Star Pyramid=sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*sqrt(Lateral Edge Length of Star Pyramid^2-(Chord Length of Star Pyramid^2/100*(50+(10*sqrt(5)))))

Can the Volume of Star Pyramid given Pentagonal Edge Length of Base be negative?

No, the Volume of Star Pyramid given Pentagonal Edge Length of Base, measured in Volume cannot be negative.

Which unit is used to measure Volume of Star Pyramid given Pentagonal Edge Length of Base?

Volume of Star Pyramid given Pentagonal Edge Length of Base 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 Star Pyramid given Pentagonal Edge Length of Base can be measured.

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Volume of Star Pyramid given Pentagonal Edge Length of Base Formula

​GoVolume of Star Pyramid Formula

​GoVolume of Star Pyramid given Edge Length of Base Formula

Volume of Star Pyramid given Pentagonal Edge Length of Base Example

Volume of Star Pyramid given Pentagonal Edge Length of Base Solution

Volume of Star Pyramid given Pentagonal Edge Length of Base Formula Elements

Other Formulas to find Volume of Star Pyramid

Other formulas in Volume and Surface to Volume Ratio of Star Pyramid category

How to Evaluate Volume of Star Pyramid given Pentagonal Edge Length of Base?

FAQs on Volume of Star Pyramid given Pentagonal Edge Length of Base

Variable Name

GoVolume of Star Pyramid Formula

GoVolume of Star Pyramid given Edge Length of Base Formula