Edge Length of Rhombohedron given Volume Calculator

✖Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the surface of the Rhombohedron.ⓘ Volume of Rhombohedron [V]			+10% -10%
✖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%

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

⎘ Copy

👎

Formula

✖

Edge Length of Rhombohedron given Volume

Formula

`"l"_{"e"} = ("V"/((1-cos("∠"_{"Acute"}))*sqrt(1+2*cos("∠"_{"Acute"}))))^(1/3)`

Example

`"9.999766m"=("540m³"/((1-cos("50°"))*sqrt(1+2*cos("50°"))))^(1/3)`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF

Edge Length of Rhombohedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Rhombohedron = (Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(1/3)
l_e = (V/((1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))))^(1/3)
This formula uses 2 Functions, 3 Variables

Functions Used

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.
Volume of Rhombohedron - (Measured in Cubic Meter) - Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the surface 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.

STEP 1: Convert Input(s) to Base Unit

Volume of Rhombohedron: 540 Cubic Meter --> 540 Cubic Meter No Conversion Required
Acute Angle of Rhombohedron: 50 Degree --> 0.872664625997001 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (V/((1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))))^(1/3) --> (540/((1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))))^(1/3)

Evaluating ... ...

l_e = 9.99976579916092

STEP 3: Convert Result to Output's Unit

9.99976579916092 Meter --> No Conversion Required

FINAL ANSWER

9.99976579916092 ≈ 9.999766 Meter <-- Edge Length of Rhombohedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Rhombohedron » Edge Length of Rhombohedron » Edge Length of Rhombohedron given Volume

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 1100+ more calculators!

< 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 Volume 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 Volume?

Edge Length of Rhombohedron given Volume calculator uses Edge Length of Rhombohedron = (Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(1/3) to calculate the Edge Length of Rhombohedron, Edge Length of Rhombohedron given Volume formula is defined as the distance between any pair of adjacent vertices of the Rhombohedron, calculated using its volume. Edge Length of Rhombohedron is denoted by l_e symbol.

How to calculate Edge Length of Rhombohedron given Volume using this online calculator? To use this online calculator for Edge Length of Rhombohedron given Volume, enter Volume of Rhombohedron (V) & Acute Angle of Rhombohedron (∠_Acute) and hit the calculate button. Here is how the Edge Length of Rhombohedron given Volume calculation can be explained with given input values -> 9.999766 = (540/((1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))))^(1/3).

FAQ

What is Edge Length of Rhombohedron given Volume?

Edge Length of Rhombohedron given Volume formula is defined as the distance between any pair of adjacent vertices of the Rhombohedron, calculated using its volume and is represented as l_e = (V/((1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))))^(1/3) or Edge Length of Rhombohedron = (Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(1/3). Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the surface of the Rhombohedron & Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees.

How to calculate Edge Length of Rhombohedron given Volume?

Edge Length of Rhombohedron given Volume formula is defined as the distance between any pair of adjacent vertices of the Rhombohedron, calculated using its volume is calculated using Edge Length of Rhombohedron = (Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(1/3). To calculate Edge Length of Rhombohedron given Volume, you need Volume of Rhombohedron (V) & Acute Angle of Rhombohedron (∠_Acute). With our tool, you need to enter the respective value for Volume of Rhombohedron & Acute Angle 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 Volume of Rhombohedron & Acute Angle 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 = (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)))

Home

FREE PDFs

🔍 Search