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Volume of Rhombohedron given Surface to Volume Ratio Formula

GoVolume of Rhombohedron Formula

GoVolume of Rhombohedron given Obtuse Angle 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 = {(\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)}

V - Volume of Rhombohedron?∠_Acute - Acute Angle of Rhombohedron?R_A/V - Surface to Volume Ratio of Rhombohedron?

Volume of Rhombohedron given Surface to Volume Ratio Example

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Here is how the Volume of Rhombohedron given Surface to Volume Ratio equation looks like with Values.

Here is how the Volume of Rhombohedron given Surface to Volume Ratio equation looks like with Units.

Here is how the Volume of Rhombohedron given Surface to Volume Ratio equation looks like.

650.2751 = {(\frac{6 \cdot \sin (50)}{0.8 \cdot (1 - \cos (50)) \cdot \sqrt{1 + 2 \cdot \cos (50)}})}^{3} \cdot (1 - \cos (50)) \cdot \sqrt{1 + 2 \cdot \cos (50)}

650.2751m³ = {(\frac{6 \cdot \sin (50°)}{0.8m⁻¹ \cdot (1 - \cos (50°)) \cdot \sqrt{1 + 2 \cdot \cos (50°)}})}^{3} \cdot (1 - \cos (50°)) \cdot \sqrt{1 + 2 \cdot \cos (50°)}

650.2751 = {(\frac{6 \cdot \sin (50)}{0.8 \cdot (1 - \cos (50)) \cdot \sqrt{1 + 2 \cdot \cos (50)}})}^{3} \cdot (1 - \cos (50)) \cdot \sqrt{1 + 2 \cdot \cos (50)}

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Volume of Rhombohedron given Surface to Volume Ratio Solution

Follow our step by step solution on how to calculate Volume of Rhombohedron given Surface to Volume Ratio?

FIRST Step Consider the formula

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)}

Next Step Substitute values of Variables

∴

V = {(\frac{6 \cdot \sin (50°)}{0.8m⁻¹ \cdot (1 - \cos (50°)) \cdot \sqrt{1 + 2 \cdot \cos (50°)}})}^{3} \cdot (1 - \cos (50°)) \cdot \sqrt{1 + 2 \cdot \cos (50°)}

Next Step Convert Units

∴

V = {(\frac{6 \cdot \sin (0.8727rad)}{0.8m⁻¹ \cdot (1 - \cos (0.8727rad)) \cdot \sqrt{1 + 2 \cdot \cos (0.8727rad)}})}^{3} \cdot (1 - \cos (0.8727rad)) \cdot \sqrt{1 + 2 \cdot \cos (0.8727rad)}

Next Step Prepare to Evaluate

∴

V = {(\frac{6 \cdot \sin (0.8727)}{0.8 \cdot (1 - \cos (0.8727)) \cdot \sqrt{1 + 2 \cdot \cos (0.8727)}})}^{3} \cdot (1 - \cos (0.8727)) \cdot \sqrt{1 + 2 \cdot \cos (0.8727)}

Next Step Evaluate

∴

V = 650.275126428375m³

LAST Step Rounding Answer

∴

V = 650.2751m³

Volume of Rhombohedron given Surface to Volume Ratio Formula Elements

Variables

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

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.

Symbol: ∠_Acute

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Acute Angle of Rhombohedron

Surface to Volume Ratio of Rhombohedron

Surface to Volume Ratio of Rhombohedron is the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Rhombohedron

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.

Syntax: sin(Angle)

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 Obtuse Angle

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

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)}

How to Evaluate Volume of Rhombohedron given Surface to Volume Ratio?

Volume of Rhombohedron given Surface to Volume Ratio evaluator uses 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)) to evaluate the Volume of Rhombohedron, Volume of Rhombohedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombohedron, calculated using its surface to volume ratio. Volume of Rhombohedron is denoted by V symbol.

How to evaluate Volume of Rhombohedron given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Volume 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.

FAQs on Volume of Rhombohedron given Surface to Volume Ratio

What is the formula to find Volume of Rhombohedron given Surface to Volume Ratio?

The formula of Volume of Rhombohedron given Surface to Volume Ratio is expressed as 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)). Here is an example- 650.2751 = ((6*sin(0.872664625997001))/(0.8*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))))^3*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001)).

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

With Acute Angle of Rhombohedron (∠_Acute) & Surface to Volume Ratio of Rhombohedron (R_A/V) we can find Volume of Rhombohedron given Surface to Volume Ratio using the formula - 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)). This formula also uses Sine (sin)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=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))

Can the Volume of Rhombohedron given Surface to Volume Ratio be negative?

No, the Volume of Rhombohedron given Surface to Volume Ratio, measured in Volume cannot be negative.

Which unit is used to measure Volume of Rhombohedron given Surface to Volume Ratio?

Volume of Rhombohedron given Surface to Volume Ratio 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 Surface to Volume Ratio can be measured.

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