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Surface to Volume Ratio of Rhombohedron given Obtuse Angle Formula

GoSurface to Volume Ratio of Rhombohedron Formula

GoSurface to Volume Ratio of Rhombohedron given Total Surface Area Formula

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

R A/V = \frac{6 \cdot \sin (π - ∠ Obtuse)}{l e \cdot (1 - \cos (π - ∠ Obtuse)) \cdot \sqrt{1 + 2 \cdot \cos (π - ∠ Obtuse)}}

R_A/V - Surface to Volume Ratio of Rhombohedron?∠_Obtuse - Obtuse Angle of Rhombohedron?l_e - Edge Length of Rhombohedron?π - Archimedes' constant?

Surface to Volume Ratio of Rhombohedron given Obtuse Angle Example

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

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

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

0.8511 = \frac{6 \cdot \sin (3.1416 - 130)}{10 \cdot (1 - \cos (3.1416 - 130)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 130)}}

0.8511m⁻¹ = \frac{6 \cdot \sin (3.1416 - 130°)}{10m \cdot (1 - \cos (3.1416 - 130°)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 130°)}}

0.8511 = \frac{6 \cdot \sin (3.1416 - 130)}{10 \cdot (1 - \cos (3.1416 - 130)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 130)}}

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Surface to Volume Ratio of Rhombohedron given Obtuse Angle Solution

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

FIRST Step Consider the formula

R A/V = \frac{6 \cdot \sin (π - ∠ Obtuse)}{l e \cdot (1 - \cos (π - ∠ Obtuse)) \cdot \sqrt{1 + 2 \cdot \cos (π - ∠ Obtuse)}}

Next Step Substitute values of Variables

∴

R A/V = \frac{6 \cdot \sin (π - 130°)}{10m \cdot (1 - \cos (π - 130°)) \cdot \sqrt{1 + 2 \cdot \cos (π - 130°)}}

Next Step Substitute values of Constants

∴

R A/V = \frac{6 \cdot \sin (3.1416 - 130°)}{10m \cdot (1 - \cos (3.1416 - 130°)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 130°)}}

Next Step Convert Units

∴

R A/V = \frac{6 \cdot \sin (3.1416 - 2.2689rad)}{10m \cdot (1 - \cos (3.1416 - 2.2689rad)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 2.2689rad)}}

Next Step Prepare to Evaluate

∴

R A/V = \frac{6 \cdot \sin (3.1416 - 2.2689)}{10 \cdot (1 - \cos (3.1416 - 2.2689)) \cdot \sqrt{1 + 2 \cdot \cos (3.1416 - 2.2689)}}

Next Step Evaluate

∴

R A/V = 0.851100691003938m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.8511m⁻¹

Surface to Volume Ratio of Rhombohedron given Obtuse Angle Formula Elements

Variables

Constants

Functions

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

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

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

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

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 Surface to Volume Ratio of Rhombohedron

Go Surface to Volume Ratio of Rhombohedron

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

Go Surface to Volume Ratio of Rhombohedron given Total Surface Area

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

Go Surface to Volume Ratio of Rhombohedron given Volume

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

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

Surface to Volume Ratio of Rhombohedron given Obtuse Angle evaluator uses Surface to Volume Ratio of Rhombohedron = (6*sin(pi-Obtuse Angle of Rhombohedron))/(Edge Length of Rhombohedron*(1-cos(pi-Obtuse Angle of Rhombohedron))*sqrt(1+2*cos(pi-Obtuse Angle of Rhombohedron))) to evaluate the Surface to Volume Ratio of Rhombohedron, Surface to Volume Ratio of Rhombohedron given Obtuse Angle formula is defined as the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron, calculated using its obtuse angle. Surface to Volume Ratio of Rhombohedron is denoted by R_A/V symbol.

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

FAQs on Surface to Volume Ratio of Rhombohedron given Obtuse Angle

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

The formula of Surface to Volume Ratio of Rhombohedron given Obtuse Angle is expressed as Surface to Volume Ratio of Rhombohedron = (6*sin(pi-Obtuse Angle of Rhombohedron))/(Edge Length of Rhombohedron*(1-cos(pi-Obtuse Angle of Rhombohedron))*sqrt(1+2*cos(pi-Obtuse Angle of Rhombohedron))). Here is an example- 0.851101 = (6*sin(pi-2.2689280275922))/(10*(1-cos(pi-2.2689280275922))*sqrt(1+2*cos(pi-2.2689280275922))).

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

With Obtuse Angle of Rhombohedron (∠_Obtuse) & Edge Length of Rhombohedron (l_e) we can find Surface to Volume Ratio of Rhombohedron given Obtuse Angle using the formula - Surface to Volume Ratio of Rhombohedron = (6*sin(pi-Obtuse Angle of Rhombohedron))/(Edge Length of Rhombohedron*(1-cos(pi-Obtuse Angle of Rhombohedron))*sqrt(1+2*cos(pi-Obtuse Angle of Rhombohedron))). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Surface to Volume Ratio of Rhombohedron?

Here are the different ways to Calculate Surface to Volume Ratio of Rhombohedron-

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

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

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

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

Surface to Volume Ratio of Rhombohedron given Obtuse Angle is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Surface to Volume Ratio of Rhombohedron given Obtuse Angle can be measured.

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