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Volume of Rhombohedron given Obtuse Angle Formula

GoVolume of Rhombohedron Formula

GoVolume of Rhombohedron given Total Surface Area Formula

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Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the surface of the Rhombohedron. Check FAQs

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

V - Volume of Rhombohedron?l_e - Edge Length of Rhombohedron?∠_Obtuse - Obtuse Angle of Rhombohedron?π - Archimedes' constant?

Volume of Rhombohedron given Obtuse Angle Example

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Here is how the Volume of Rhombohedron given Obtuse Angle equation looks like with Values.

Here is how the Volume of Rhombohedron given Obtuse Angle equation looks like with Units.

Here is how the Volume of Rhombohedron given Obtuse Angle equation looks like.

540.0379 = 10^{3} \cdot (1 - \cos (3.1416 - 130)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 130)}

540.0379m³ = {10m}^{3} \cdot (1 - \cos (3.1416 - 130°)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 130°)}

540.0379 = 10^{3} \cdot (1 - \cos (3.1416 - 130)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 130)}

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Volume of Rhombohedron given Obtuse Angle Solution

Follow our step by step solution on how to calculate Volume of Rhombohedron given Obtuse Angle?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = {10m}^{3} \cdot (1 - \cos (π - 130°)) \cdot \sqrt{1 + 2 \cdot \cos (π - 130°)}

Next Step Substitute values of Constants

∴

V = {10m}^{3} \cdot (1 - \cos (3.1416 - 130°)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 130°)}

Next Step Convert Units

∴

V = {10m}^{3} \cdot (1 - \cos (3.1416 - 2.2689rad)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 2.2689rad)}

Next Step Prepare to Evaluate

∴

V = 10^{3} \cdot (1 - \cos (3.1416 - 2.2689)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 2.2689)}

Next Step Evaluate

∴

V = 540.03794231372m³

LAST Step Rounding Answer

∴

V = 540.0379m³

Volume of Rhombohedron given Obtuse Angle Formula Elements

Variables

Constants

Functions

Volume of Rhombohedron

Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the surface of the Rhombohedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Rhombohedron

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

Obtuse Angle of Rhombohedron

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

Symbol: ∠_Obtuse

Measurement: AngleUnit: °

Note: Value should be between 90 to 180.

Formulas to find Obtuse Angle of Rhombohedron

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 Volume of Rhombohedron

Go Volume of Rhombohedron

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

Go Volume of Rhombohedron given Total Surface Area

V = {(\sqrt{\frac{TSA}{6 \cdot \sin (∠ Acute)}})}^{3} \cdot (1 - \cos (∠ Acute)) \cdot \sqrt{1 + 2 \cdot \cos (∠ Acute)}

Go Volume of Rhombohedron given Surface to Volume Ratio

V = {(\frac{6 \cdot \sin (∠ Acute)}{R A/V \cdot (1 - \cos (∠ Acute)) \cdot \sqrt{1 + 2 \cdot \cos (∠ Acute)}})}^{3} \cdot (1 - \cos (∠ Acute)) \cdot \sqrt{1 + 2 \cdot \cos (∠ Acute)}

How to Evaluate Volume of Rhombohedron given Obtuse Angle?

Volume of Rhombohedron given Obtuse Angle evaluator 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 evaluate 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 evaluate Volume of Rhombohedron given Obtuse Angle using this online evaluator? To use this online evaluator for Volume of Rhombohedron given Obtuse Angle, enter Edge Length of Rhombohedron (l_e) & Obtuse Angle of Rhombohedron (∠_Obtuse) and hit the calculate button.

FAQs on Volume of Rhombohedron given Obtuse Angle

What is the formula to find Volume of Rhombohedron given Obtuse Angle?

The formula of Volume of Rhombohedron given Obtuse Angle is expressed as Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(pi-Obtuse Angle of Rhombohedron))*sqrt(1+2*cos(pi-Obtuse Angle of Rhombohedron)). Here is an example- 540.0379 = 10^3*(1-cos(pi-2.2689280275922))*sqrt(1+2*cos(pi-2.2689280275922)).

How to calculate Volume of Rhombohedron given Obtuse Angle?

With Edge Length of Rhombohedron (l_e) & Obtuse Angle of Rhombohedron (∠_Obtuse) we can find Volume of Rhombohedron given Obtuse Angle using the formula - Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(pi-Obtuse Angle of Rhombohedron))*sqrt(1+2*cos(pi-Obtuse Angle of Rhombohedron)). This formula also uses Archimedes' constant and , Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Rhombohedron?

Here are the different ways to Calculate Volume of Rhombohedron-

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))

Can the Volume of Rhombohedron given Obtuse Angle be negative?

No, the Volume of Rhombohedron given Obtuse Angle, measured in Volume cannot be negative.

Which unit is used to measure Volume of Rhombohedron given Obtuse Angle?

Volume of Rhombohedron given Obtuse Angle is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Rhombohedron given Obtuse Angle can be measured.

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