Volume of Rhombohedron Calculator

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

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

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Formula

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Volume of Rhombohedron

Formula

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

Example

`"540.0379m³"=("10m")^3*(1-cos("50°"))*sqrt(1+2*cos("50°"))`

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Volume of Rhombohedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))
V = l_e^3*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))
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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Rhombohedron: 10 Meter --> 10 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

V = l_e^3*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute)) --> 10^3*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))

Evaluating ... ...

V = 540.037942313142

STEP 3: Convert Result to Output's Unit

540.037942313142 Cubic Meter --> No Conversion Required

FINAL ANSWER

540.037942313142 ≈ 540.0379 Cubic Meter <-- Volume of Rhombohedron

(Calculation completed in 00.021 seconds)

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< 4 Volume of Rhombohedron Calculators

Volume of Rhombohedron given Surface to Volume Ratio

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

Volume of Rhombohedron given Total Surface Area

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

Volume of Rhombohedron given Obtuse Angle

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

Volume of Rhombohedron

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

Volume of Rhombohedron Formula

Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))
V = l_e^3*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))

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 Volume of Rhombohedron?

Volume of Rhombohedron calculator uses Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron)) to calculate the Volume of Rhombohedron, Volume of Rhombohedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombohedron. Volume of Rhombohedron is denoted by V symbol.

How to calculate Volume of Rhombohedron using this online calculator? To use this online calculator for Volume of Rhombohedron, enter Edge Length of Rhombohedron (l_e) & Acute Angle of Rhombohedron (∠_Acute) and hit the calculate button. Here is how the Volume of Rhombohedron calculation can be explained with given input values -> 540.0379 = 10^3*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001)).

FAQ

What is Volume of Rhombohedron?

Volume of Rhombohedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombohedron and is represented as V = l_e^3*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute)) or Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron)). Edge Length of Rhombohedron is the distance between any pair of adjacent vertices 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 Volume of Rhombohedron?

Volume of Rhombohedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombohedron is calculated using Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron)). To calculate Volume of Rhombohedron, you need Edge Length of Rhombohedron (l_e) & Acute Angle of Rhombohedron (∠_Acute). With our tool, you need to enter the respective value for Edge Length 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 Volume of Rhombohedron?

In this formula, Volume of Rhombohedron uses Edge Length of Rhombohedron & Acute Angle of Rhombohedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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