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Edge Length of Truncated Rhombohedron given Surface to Volume Ratio Formula

GoEdge Length of Truncated Rhombohedron given Rhombohedral Edge Length Formula

GoEdge Length of Truncated Rhombohedron given Triangular Edge Length Formula

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Edge Length of Truncated Rhombohedron is the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron. Check FAQs

l e = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2 \cdot (\frac{5}{3}) \cdot (\sqrt{\sqrt{5} - 2}) \cdot R A/V})

l_e - Edge Length of Truncated Rhombohedron?R_A/V - Surface to Volume Ratio of Truncated Rhombohedron?

Edge Length of Truncated Rhombohedron given Surface to Volume Ratio Example

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Here is how the Edge Length of Truncated Rhombohedron given Surface to Volume Ratio equation looks like with Values.

Here is how the Edge Length of Truncated Rhombohedron given Surface to Volume Ratio equation looks like with Units.

Here is how the Edge Length of Truncated Rhombohedron given Surface to Volume Ratio equation looks like.

11.966 = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2 \cdot (\frac{5}{3}) \cdot (\sqrt{\sqrt{5} - 2}) \cdot 0.2})

11.966m = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2 \cdot (\frac{5}{3}) \cdot (\sqrt{\sqrt{5} - 2}) \cdot 0.2m⁻¹})

11.966 = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2 \cdot (\frac{5}{3}) \cdot (\sqrt{\sqrt{5} - 2}) \cdot 0.2})

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Edge Length of Truncated Rhombohedron given Surface to Volume Ratio Solution

Follow our step by step solution on how to calculate Edge Length of Truncated Rhombohedron given Surface to Volume Ratio?

FIRST Step Consider the formula

l e = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2 \cdot (\frac{5}{3}) \cdot (\sqrt{\sqrt{5} - 2}) \cdot R A/V})

Next Step Substitute values of Variables

∴

l e = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2 \cdot (\frac{5}{3}) \cdot (\sqrt{\sqrt{5} - 2}) \cdot 0.2m⁻¹})

Next Step Prepare to Evaluate

∴

l e = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2 \cdot (\frac{5}{3}) \cdot (\sqrt{\sqrt{5} - 2}) \cdot 0.2})

Next Step Evaluate

∴

l e = 11.9660155731459m

LAST Step Rounding Answer

∴

l e = 11.966m

Edge Length of Truncated Rhombohedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Edge Length of Truncated Rhombohedron

Edge Length of Truncated Rhombohedron is the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Truncated Rhombohedron

Surface to Volume Ratio of Truncated Rhombohedron

Surface to Volume Ratio of Truncated Rhombohedron is the numerical ratio of the total surface area of a Truncated Rhombohedron to the volume of the Truncated Rhombohedron.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Truncated Rhombohedron

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 Edge Length of Truncated Rhombohedron

Go Edge Length of Truncated Rhombohedron given Rhombohedral Edge Length

l e = \frac{l e(Rhombohedron) \cdot (3 - \sqrt{5})}{2}

Go Edge Length of Truncated Rhombohedron given Triangular Edge Length

l e = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{l e(Triangle)}{\sqrt{5 - (2 \cdot \sqrt{5})}})

Go Edge Length of Truncated Rhombohedron given Circumsphere Radius

l e = (\frac{3 - \sqrt{5}}{2}) \cdot (\frac{4 \cdot r c}{\sqrt{14 - (2 \cdot \sqrt{5})}})

Go Edge Length of Truncated Rhombohedron given Total Surface Area

l e = (\frac{3 - \sqrt{5}}{2}) \cdot (\sqrt{\frac{2 \cdot TSA}{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}})

How to Evaluate Edge Length of Truncated Rhombohedron given Surface to Volume Ratio?

Edge Length of Truncated Rhombohedron given Surface to Volume Ratio evaluator uses Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*(((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*(5/3)*(sqrt(sqrt(5)-2))*Surface to Volume Ratio of Truncated Rhombohedron)) to evaluate the Edge Length of Truncated Rhombohedron, Edge Length of Truncated Rhombohedron given Surface to Volume Ratio formula is defined as the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron, calculated using its surface to volume ratio. Edge Length of Truncated Rhombohedron is denoted by l_e symbol.

How to evaluate Edge Length of Truncated Rhombohedron given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Edge Length of Truncated Rhombohedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Truncated Rhombohedron (R_A/V) and hit the calculate button.

FAQs on Edge Length of Truncated Rhombohedron given Surface to Volume Ratio

What is the formula to find Edge Length of Truncated Rhombohedron given Surface to Volume Ratio?

The formula of Edge Length of Truncated Rhombohedron given Surface to Volume Ratio is expressed as Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*(((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*(5/3)*(sqrt(sqrt(5)-2))*Surface to Volume Ratio of Truncated Rhombohedron)). Here is an example- 11.96602 = ((3-sqrt(5))/2)*(((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*(5/3)*(sqrt(sqrt(5)-2))*0.2)).

How to calculate Edge Length of Truncated Rhombohedron given Surface to Volume Ratio?

With Surface to Volume Ratio of Truncated Rhombohedron (R_A/V) we can find Edge Length of Truncated Rhombohedron given Surface to Volume Ratio using the formula - Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*(((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*(5/3)*(sqrt(sqrt(5)-2))*Surface to Volume Ratio of Truncated Rhombohedron)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Edge Length of Truncated Rhombohedron?

Here are the different ways to Calculate Edge Length of Truncated Rhombohedron-

Edge Length of Truncated Rhombohedron=(Rhombohedral Edge Length of Truncated Rhombohedron*(3-sqrt(5)))/2
Edge Length of Truncated Rhombohedron=((3-sqrt(5))/2)*(Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))
Edge Length of Truncated Rhombohedron=((3-sqrt(5))/2)*((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))

Can the Edge Length of Truncated Rhombohedron given Surface to Volume Ratio be negative?

No, the Edge Length of Truncated Rhombohedron given Surface to Volume Ratio, measured in Length cannot be negative.

Which unit is used to measure Edge Length of Truncated Rhombohedron given Surface to Volume Ratio?

Edge Length of Truncated Rhombohedron given Surface to Volume Ratio is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Edge Length of Truncated Rhombohedron given Surface to Volume Ratio can be measured.

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