Edge Length of Rhombohedron given Surface to Volume Ratio Calculator

✖Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees.ⓘ Acute Angle of Rhombohedron [∠_Acute]			+10% -10%
✖Surface to Volume Ratio of Rhombohedron is the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron.ⓘ Surface to Volume Ratio of Rhombohedron [R_A/V]			+10% -10%

✖Edge Length of Rhombohedron is the distance between any pair of adjacent vertices of the Rhombohedron.ⓘ Edge Length of Rhombohedron given Surface to Volume Ratio [l_e]

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Formula

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Edge Length of Rhombohedron given Surface to Volume Ratio

Formula

`"l"_{"e"} = (6*sin("∠"_{"Acute"}))/("R"_{"A/V"}*(1-cos("∠"_{"Acute"}))*sqrt(1+2*cos("∠"_{"Acute"})))`

Example

`"10.63876m"=(6*sin("50°"))/("0.8m⁻¹"*(1-cos("50°"))*sqrt(1+2*cos("50°")))`

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Edge Length of Rhombohedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
l_e = (6*sin(∠_Acute))/(R_A/V*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute)))
This formula uses 3 Functions, 3 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., sqrt(Number)

Variables Used

Edge Length of Rhombohedron - (Measured in Meter) - Edge Length of Rhombohedron is the distance between any pair of adjacent vertices of the Rhombohedron.
Acute Angle of Rhombohedron - (Measured in Radian) - Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees.
Surface to Volume Ratio of Rhombohedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Rhombohedron is the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron.

STEP 1: Convert Input(s) to Base Unit

Acute Angle of Rhombohedron: 50 Degree --> 0.872664625997001 Radian (Check conversion here)
Surface to Volume Ratio of Rhombohedron: 0.8 1 per Meter --> 0.8 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (6*sin(∠_Acute))/(R_A/V*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))) --> (6*sin(0.872664625997001))/(0.8*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001)))

Evaluating ... ...

l_e = 10.6387586375553

STEP 3: Convert Result to Output's Unit

10.6387586375553 Meter --> No Conversion Required

FINAL ANSWER

10.6387586375553 ≈ 10.63876 Meter <-- Edge Length of Rhombohedron

(Calculation completed in 00.004 seconds)

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< 3 Edge Length of Rhombohedron Calculators

Edge Length of Rhombohedron given Surface to Volume Ratio

Go 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)))

Edge Length of Rhombohedron given Volume

Go Edge Length of Rhombohedron = (Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(1/3)

Edge Length of Rhombohedron given Total Surface Area

Go Edge Length of Rhombohedron = sqrt(Total Surface Area of Rhombohedron/(6*sin(Acute Angle of Rhombohedron)))

Edge Length of Rhombohedron given Surface to Volume Ratio Formula

What is a Rhombohedron?

A Rhombohedron (also called a rhombic hexahedron) is a three-dimensional figure like a cuboid (also called a rectangular parallelepiped), except that its faces are not rectangles but rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. In general, a Rhombohedron can have up to three types of rhombic faces in congruent opposite pairs, Ci symmetry, order 2.

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

Edge Length of Rhombohedron given Surface to Volume Ratio calculator 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 calculate 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 calculate Edge Length of Rhombohedron given Surface to Volume Ratio using this online calculator? To use this online calculator 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. Here is how the Edge Length of Rhombohedron given Surface to Volume Ratio calculation can be explained with given input values -> 10.63876 = (6*sin(0.872664625997001))/(0.8*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))).

FAQ

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

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 and is represented as l_e = (6*sin(∠_Acute))/(R_A/V*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))) or 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))). Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees & Surface to Volume Ratio of Rhombohedron is the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron.

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

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 is calculated using 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 calculate Edge Length of Rhombohedron given Surface to Volume Ratio, you need Acute Angle of Rhombohedron (∠_Acute) & Surface to Volume Ratio of Rhombohedron (R_A/V). With our tool, you need to enter the respective value for Acute Angle of Rhombohedron & Surface to Volume Ratio of Rhombohedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Edge Length of Rhombohedron?

In this formula, Edge Length of Rhombohedron uses Acute Angle of Rhombohedron & Surface to Volume Ratio of Rhombohedron. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)

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