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Edge Length of Rhombohedron given Surface to Volume Ratio Formula

GoEdge Length of Rhombohedron given Total Surface Area Formula

GoEdge Length of Rhombohedron given Volume Formula

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Edge Length of Rhombohedron is the distance between any pair of adjacent vertices of the Rhombohedron. Check FAQs

l e = \frac{6 \cdot \sin (∠ Acute)}{R A/V \cdot (1 - \cos (∠ Acute)) \cdot \sqrt{1 + 2 \cdot \cos (∠ Acute)}}

l_e - Edge Length of Rhombohedron?∠_Acute - Acute Angle of Rhombohedron?R_A/V - Surface to Volume Ratio of Rhombohedron?

Edge Length of Rhombohedron given Surface to Volume Ratio Example

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

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

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

10.6388 = \frac{6 \cdot \sin (50)}{0.8 \cdot (1 - \cos (50)) \cdot \sqrt{1 + 2 \cdot \cos (50)}}

10.6388m = \frac{6 \cdot \sin (50°)}{0.8m⁻¹ \cdot (1 - \cos (50°)) \cdot \sqrt{1 + 2 \cdot \cos (50°)}}

10.6388 = \frac{6 \cdot \sin (50)}{0.8 \cdot (1 - \cos (50)) \cdot \sqrt{1 + 2 \cdot \cos (50)}}

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Edge Length of Rhombohedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

l e = \frac{6 \cdot \sin (∠ Acute)}{R A/V \cdot (1 - \cos (∠ Acute)) \cdot \sqrt{1 + 2 \cdot \cos (∠ Acute)}}

Next Step Substitute values of Variables

∴

l e = \frac{6 \cdot \sin (50°)}{0.8m⁻¹ \cdot (1 - \cos (50°)) \cdot \sqrt{1 + 2 \cdot \cos (50°)}}

Next Step Convert Units

∴

l e = \frac{6 \cdot \sin (0.8727rad)}{0.8m⁻¹ \cdot (1 - \cos (0.8727rad)) \cdot \sqrt{1 + 2 \cdot \cos (0.8727rad)}}

Next Step Prepare to Evaluate

∴

l e = \frac{6 \cdot \sin (0.8727)}{0.8 \cdot (1 - \cos (0.8727)) \cdot \sqrt{1 + 2 \cdot \cos (0.8727)}}

Next Step Evaluate

∴

l e = 10.6387586375553m

LAST Step Rounding Answer

∴

l e = 10.6388m

Edge Length of Rhombohedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Edge Length of Rhombohedron

Edge Length of Rhombohedron is the distance between any pair of adjacent vertices of the Rhombohedron.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Rhombohedron

Acute Angle of Rhombohedron

Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees.

Symbol: ∠_Acute

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Acute Angle of Rhombohedron

Surface to Volume Ratio of Rhombohedron

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

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 Rhombohedron

Go Edge Length of Rhombohedron given Total Surface Area

l e = \sqrt{\frac{TSA}{6 \cdot \sin (∠ Acute)}}

Go Edge Length of Rhombohedron given Volume

l e = {(\frac{V}{(1 - \cos (∠ Acute)) \cdot \sqrt{1 + 2 \cdot \cos (∠ Acute)}})}^{\frac{1}{3}}

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

Edge Length of Rhombohedron given Surface to Volume Ratio evaluator uses Edge Length of Rhombohedron = (6*sin(Acute Angle of Rhombohedron))/(Surface to Volume Ratio of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))) to evaluate the Edge Length of Rhombohedron, Edge Length of Rhombohedron given Surface to Volume Ratio formula is defined as the distance between any pair of adjacent vertices of the Rhombohedron, calculated using its surface to volume ratio. Edge Length of Rhombohedron is denoted by l_e symbol.

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

FAQs on Edge Length of Rhombohedron given Surface to Volume Ratio

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

The formula of Edge Length of Rhombohedron given Surface to Volume Ratio is expressed as Edge Length of Rhombohedron = (6*sin(Acute Angle of Rhombohedron))/(Surface to Volume Ratio of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))). Here is an example- 10.63876 = (6*sin(0.872664625997001))/(0.8*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))).

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

With Acute Angle of Rhombohedron (∠_Acute) & Surface to Volume Ratio of Rhombohedron (R_A/V) we can find Edge Length of Rhombohedron given Surface to Volume Ratio using the formula - Edge Length of Rhombohedron = (6*sin(Acute Angle of Rhombohedron))/(Surface to Volume Ratio of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))). This formula also uses Sine (sin)Cosine (cos), Square Root (sqrt) function(s).

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

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

Edge Length of Rhombohedron=sqrt(Total Surface Area of Rhombohedron/(6*sin(Acute Angle of Rhombohedron)))
Edge Length of Rhombohedron=(Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(1/3)

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

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

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

Edge Length of 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 Rhombohedron given Surface to Volume Ratio can be measured.

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