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Surface to Volume Ratio of Star Pyramid Formula

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Surface to Volume Ratio of Star Pyramid is the numerical ratio of the total surface area of the Star Pyramid to the volume of the Star Pyramid. Check FAQs

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}

R_A/V - Surface to Volume Ratio of Star Pyramid?l_c - Chord Length of Star Pyramid?l_e(Base) - Edge Length of Base of Star Pyramid?l_e(Lateral) - Lateral Edge Length of Star Pyramid?l_e(Ridge) - Ridge Length of Star Pyramid?h - Height of Star Pyramid?

Surface to Volume Ratio of Star Pyramid Example

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Here is how the Surface to Volume Ratio of Star Pyramid equation looks like with Values.

Here is how the Surface to Volume Ratio of Star Pyramid equation looks like with Units.

Here is how the Surface to Volume Ratio of Star Pyramid equation looks like.

1.6642 = \frac{(\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})}{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{6} \cdot 7}

1.6642m⁻¹ = \frac{(\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{10m}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6m + 11m + 8m}{2}) \cdot (\frac{11m + 8m - 6m}{2}) \cdot (\frac{6m - 11m + 8m}{2}) \cdot (\frac{6m + 11m - 8m}{2})})}{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{10m}^{2}}{6} \cdot 7m}

1.6642 = \frac{(\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})}{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{6} \cdot 7}

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Surface to Volume Ratio of Star Pyramid Solution

Follow our step by step solution on how to calculate Surface to Volume Ratio of Star Pyramid?

FIRST Step Consider the formula

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}

Next Step Substitute values of Variables

∴

R A/V = \frac{(\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{10m}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6m + 11m + 8m}{2}) \cdot (\frac{11m + 8m - 6m}{2}) \cdot (\frac{6m - 11m + 8m}{2}) \cdot (\frac{6m + 11m - 8m}{2})})}{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{10m}^{2}}{6} \cdot 7m}

Next Step Prepare to Evaluate

∴

R A/V = \frac{(\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})}{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{6} \cdot 7}

Next Step Evaluate

∴

R A/V = 1.66415105545906m⁻¹

LAST Step Rounding Answer

∴

R A/V = 1.6642m⁻¹

Surface to Volume Ratio of Star Pyramid Formula Elements

Variables

Functions

Surface to Volume Ratio of Star Pyramid

Surface to Volume Ratio of Star Pyramid is the numerical ratio of the total surface area of the Star Pyramid to the volume of the Star Pyramid.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio 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

Edge Length of Base of Star Pyramid

Edge Length of Base of Star Pyramid is the length of the line joining any two adjacent vertices of the pentagrammic base of the Star Pyramid.

Symbol: l_e(Base)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Base 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

Ridge Length of Star Pyramid

Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid.

Symbol: l_e(Ridge)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Ridge Length 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

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 in Volume and Surface to Volume Ratio of Star Pyramid category

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

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})))}

How to Evaluate Surface to Volume Ratio of Star Pyramid?

Surface to Volume Ratio of Star Pyramid evaluator uses Surface to Volume Ratio of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))))/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*Height of Star Pyramid) to evaluate the Surface to Volume Ratio of Star Pyramid, Surface to volume ratio of Star Pyramid formula is defined as the numerical ratio of the total surface area of the Star Pyramid to the volume of the Star Pyramid and is calculated using the point edge, point chord, point length, height and ridge length of the Star Pyramid. Surface to Volume Ratio of Star Pyramid is denoted by R_A/V symbol.

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

FAQs on Surface to Volume Ratio of Star Pyramid

What is the formula to find Surface to Volume Ratio of Star Pyramid?

The formula of Surface to Volume Ratio of Star Pyramid is expressed as Surface to Volume Ratio of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))))/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*Height of Star Pyramid). Here is an example- 1.664151 = ((sqrt(5*(5-(2*sqrt(5))))*(10^2)/2)+(10*sqrt(((6+11+8)/2)*((11+8-6)/2)*((6-11+8)/2)*((6+11-8)/2))))/(sqrt(5*(5-(2*sqrt(5))))*10^2/6*7).

How to calculate Surface to Volume Ratio of Star Pyramid?

With Chord Length of Star Pyramid (l_c), Edge Length of Base of Star Pyramid (l_e(Base)), Lateral Edge Length of Star Pyramid (l_e(Lateral)), Ridge Length of Star Pyramid (l_e(Ridge)) & Height of Star Pyramid (h) we can find Surface to Volume Ratio of Star Pyramid using the formula - Surface to Volume Ratio of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))))/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*Height of Star Pyramid). This formula also uses Square Root (sqrt) function(s).

Can the Surface to Volume Ratio of Star Pyramid be negative?

No, the Surface to Volume Ratio of Star Pyramid, measured in Reciprocal Length cannot be negative.

Which unit is used to measure Surface to Volume Ratio of Star Pyramid?

Surface to Volume Ratio of Star Pyramid is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Surface to Volume Ratio of Star Pyramid can be measured.

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Surface to Volume Ratio of Star Pyramid Formula

Surface to Volume Ratio of Star Pyramid Example

Surface to Volume Ratio of Star Pyramid Solution

Surface to Volume Ratio of Star Pyramid Formula Elements

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

How to Evaluate Surface to Volume Ratio of Star Pyramid?

FAQs on Surface to Volume Ratio of Star Pyramid

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