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Volume of Star Pyramid given Lateral Edge Length Formula

GoVolume of Star Pyramid Formula

GoVolume of Star Pyramid given Pentagonal 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 c}^{2}}{6} \cdot \sqrt{{l e(Lateral)}^{2} - (\frac{{l c}^{2}}{100} \cdot (50 + (10 \cdot \sqrt{5})))}

V - Volume of Star Pyramid?l_c - Chord Length of Star Pyramid?l_e(Lateral) - Lateral Edge Length of Star Pyramid?

Volume of Star Pyramid given Lateral Edge Length Example

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

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

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

188.8376 = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{6} \cdot \sqrt{11^{2} - (\frac{10^{2}}{100} \cdot (50 + (10 \cdot \sqrt{5})))}

188.8376m³ = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{10m}^{2}}{6} \cdot \sqrt{{11m}^{2} - (\frac{{10m}^{2}}{100} \cdot (50 + (10 \cdot \sqrt{5})))}

188.8376 = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{6} \cdot \sqrt{11^{2} - (\frac{10^{2}}{100} \cdot (50 + (10 \cdot \sqrt{5})))}

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Volume of Star Pyramid given Lateral Edge Length Solution

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

FIRST Step Consider the formula

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})))}

Next Step Substitute values of Variables

∴

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{10m}^{2}}{6} \cdot \sqrt{{11m}^{2} - (\frac{{10m}^{2}}{100} \cdot (50 + (10 \cdot \sqrt{5})))}

Next Step Prepare to Evaluate

∴

V = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{6} \cdot \sqrt{11^{2} - (\frac{10^{2}}{100} \cdot (50 + (10 \cdot \sqrt{5})))}

Next Step Evaluate

∴

V = 188.837629842414m³

LAST Step Rounding Answer

∴

V = 188.8376m³

Volume of Star Pyramid given Lateral Edge Length Formula Elements

Variables

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

Chord Length of Star Pyramid

Chord Length of Star Pyramid is the length of the straight line joining two adjacent spike points or outer vertices of the base of the Star Pyramid.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Star Pyramid

Lateral Edge Length of Star Pyramid

Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid.

Symbol: l_e(Lateral)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Lateral Edge Length of Star Pyramid

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 Pentagonal Edge Length of Base

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

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 Lateral Edge Length?

Volume of Star Pyramid given Lateral Edge Length evaluator uses 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))))) to evaluate the Volume of Star Pyramid, Volume of Star Pyramid given Lateral Edge Length formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid and is calculated using the lateral edge length, and chord length of the Star Pyramid. Volume of Star Pyramid is denoted by V symbol.

How to evaluate Volume of Star Pyramid given Lateral Edge Length using this online evaluator? To use this online evaluator for Volume of Star Pyramid given Lateral Edge Length, enter Chord Length of Star Pyramid (l_c) & Lateral Edge Length of Star Pyramid (l_e(Lateral)) and hit the calculate button.

FAQs on Volume of Star Pyramid given Lateral Edge Length

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

The formula of Volume of Star Pyramid given Lateral Edge Length is expressed as 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))))). Here is an example- 188.8376 = sqrt(5*(5-(2*sqrt(5))))*10^2/6*sqrt(11^2-(10^2/100*(50+(10*sqrt(5))))).

How to calculate Volume of Star Pyramid given Lateral Edge Length?

With Chord Length of Star Pyramid (l_c) & Lateral Edge Length of Star Pyramid (l_e(Lateral)) we can find Volume of Star Pyramid given Lateral Edge Length using the formula - 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))))). This formula also uses 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))))*((Pentagonal Edge Length of Base of Star Pyramid*[phi]^2)^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

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

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

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

Volume of Star Pyramid given Lateral Edge Length 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 Lateral Edge Length can be measured.

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Volume of Star Pyramid given Lateral Edge Length Formula

​GoVolume of Star Pyramid Formula

​GoVolume of Star Pyramid given Pentagonal Edge Length of Base Formula

Volume of Star Pyramid given Lateral Edge Length Example

Volume of Star Pyramid given Lateral Edge Length Solution

Volume of Star Pyramid given Lateral Edge Length 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 Lateral Edge Length?

FAQs on Volume of Star Pyramid given Lateral Edge Length

Variable Name

GoVolume of Star Pyramid Formula

GoVolume of Star Pyramid given Pentagonal Edge Length of Base Formula