Volume of Rhombohedron given Obtuse Angle 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%
✖Obtuse Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is greater than 90 degrees.ⓘ Obtuse Angle of Rhombohedron [∠_Obtuse]			+10% -10%

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

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Volume of Rhombohedron given Obtuse Angle

Formula

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

Example

`"540.0379m³"=("10m")^3*(1-cos(pi-"130°"))*sqrt(1+2*cos(pi-"130°"))`

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Volume of Rhombohedron given Obtuse Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(pi-Obtuse Angle of Rhombohedron))*sqrt(1+2*cos(pi-Obtuse Angle of Rhombohedron))
V = l_e^3*(1-cos(pi-∠_Obtuse))*sqrt(1+2*cos(pi-∠_Obtuse))
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Obtuse Angle of Rhombohedron - (Measured in Radian) - Obtuse Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is greater than 90 degrees.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Rhombohedron: 10 Meter --> 10 Meter No Conversion Required
Obtuse Angle of Rhombohedron: 130 Degree --> 2.2689280275922 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = l_e^3*(1-cos(pi-∠_Obtuse))*sqrt(1+2*cos(pi-∠_Obtuse)) --> 10^3*(1-cos(pi-2.2689280275922))*sqrt(1+2*cos(pi-2.2689280275922))

Evaluating ... ...

V = 540.03794231372

STEP 3: Convert Result to Output's Unit

540.03794231372 Cubic Meter --> No Conversion Required

FINAL ANSWER

540.03794231372 ≈ 540.0379 Cubic Meter <-- Volume of Rhombohedron

(Calculation completed in 00.004 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 given Obtuse Angle 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 Volume of Rhombohedron given Obtuse Angle?

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

How to calculate Volume of Rhombohedron given Obtuse Angle using this online calculator? To use this online calculator for Volume of Rhombohedron given Obtuse Angle, enter Edge Length of Rhombohedron (l_e) & Obtuse Angle of Rhombohedron (∠_Obtuse) and hit the calculate button. Here is how the Volume of Rhombohedron given Obtuse Angle calculation can be explained with given input values -> 540.0379 = 10^3*(1-cos(pi-2.2689280275922))*sqrt(1+2*cos(pi-2.2689280275922)).

FAQ

What is Volume of Rhombohedron given Obtuse Angle?

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

How to calculate Volume of Rhombohedron given Obtuse Angle?

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