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Volume of Rhombohedral cell Formula

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Volume is the amount of space that a substance or object occupies or that is enclosed within a container. Check FAQs

V T = ({a lattice}^{3}) \cdot \sqrt{1 - (3 \cdot ({\cos (α)}^{2})) + (2 \cdot ({\cos (α)}^{3}))}

V_T - Volume?a_lattice - Lattice Constant a?α - Lattice parameter alpha?

Volume of Rhombohedral cell Example

With values

With units

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Here is how the Volume of Rhombohedral cell equation looks like with Values.

Here is how the Volume of Rhombohedral cell equation looks like with Units.

Here is how the Volume of Rhombohedral cell equation looks like.

6.1E-28 = (14^{3}) \cdot \sqrt{1 - (3 \cdot ({\cos (30)}^{2})) + (2 \cdot ({\cos (30)}^{3}))}

6.1E-28m³ = ({14A}^{3}) \cdot \sqrt{1 - (3 \cdot ({\cos (30°)}^{2})) + (2 \cdot ({\cos (30°)}^{3}))}

6.1E-28 = (14^{3}) \cdot \sqrt{1 - (3 \cdot ({\cos (30)}^{2})) + (2 \cdot ({\cos (30)}^{3}))}

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Volume of Different Cubic Cell » fx Volume of Rhombohedral cell

Volume of Rhombohedral cell Solution

Follow our step by step solution on how to calculate Volume of Rhombohedral cell?

FIRST Step Consider the formula

V T = ({a lattice}^{3}) \cdot \sqrt{1 - (3 \cdot ({\cos (α)}^{2})) + (2 \cdot ({\cos (α)}^{3}))}

Next Step Substitute values of Variables

∴

V T = ({14A}^{3}) \cdot \sqrt{1 - (3 \cdot ({\cos (30°)}^{2})) + (2 \cdot ({\cos (30°)}^{3}))}

Next Step Convert Units

∴

V T = ({1.4E-9m}^{3}) \cdot \sqrt{1 - (3 \cdot ({\cos (0.5236rad)}^{2})) + (2 \cdot ({\cos (0.5236rad)}^{3}))}

Next Step Prepare to Evaluate

∴

V T = ({1.4E-9}^{3}) \cdot \sqrt{1 - (3 \cdot ({\cos (0.5236)}^{2})) + (2 \cdot ({\cos (0.5236)}^{3}))}

Next Step Evaluate

∴

V T = 6.07646428496212E-28m³

LAST Step Rounding Answer

∴

V T = 6.1E-28m³

Volume of Rhombohedral cell Formula Elements

Variables

Functions

Volume

Volume is the amount of space that a substance or object occupies or that is enclosed within a container.

Symbol: V_T

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume

Lattice Constant a

The Lattice Constant a refers to the physical dimension of unit cells in a crystal lattice along x-axis.

Symbol: a_lattice

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Lattice Constant a

Lattice parameter alpha

The Lattice parameter alpha is the angle between lattice constants b and c.

Symbol: α

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Lattice parameter alpha

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

Go Volume of Unit cell

V T = a^{3}

Go Volume of Simple Cubic Unit Cell

V T = {(2 \cdot R)}^{3}

Go Volume of Body Centered Unit Cell

V T = {(4 \cdot \frac{R}{\sqrt{3}})}^{3}

Go Volume of face Centered Unit Cell

V T = {(2 \cdot \sqrt{2} \cdot R)}^{3}

How to Evaluate Volume of Rhombohedral cell?

Volume of Rhombohedral cell evaluator uses Volume = (Lattice Constant a^3)*sqrt(1-(3*(cos(Lattice parameter alpha)^2))+(2*(cos(Lattice parameter alpha)^3))) to evaluate the Volume, The Volume of Rhombohedral cell formula is defined as the space occupied by an Rhombohedral crystal lattice. Volume is denoted by V_T symbol.

How to evaluate Volume of Rhombohedral cell using this online evaluator? To use this online evaluator for Volume of Rhombohedral cell, enter Lattice Constant a (a_lattice) & Lattice parameter alpha (α) and hit the calculate button.

FAQs on Volume of Rhombohedral cell

What is the formula to find Volume of Rhombohedral cell?

The formula of Volume of Rhombohedral cell is expressed as Volume = (Lattice Constant a^3)*sqrt(1-(3*(cos(Lattice parameter alpha)^2))+(2*(cos(Lattice parameter alpha)^3))). Here is an example- 6.1E-28 = (1.4E-09^3)*sqrt(1-(3*(cos(0.5235987755982)^2))+(2*(cos(0.5235987755982)^3))).

How to calculate Volume of Rhombohedral cell?

With Lattice Constant a (a_lattice) & Lattice parameter alpha (α) we can find Volume of Rhombohedral cell using the formula - Volume = (Lattice Constant a^3)*sqrt(1-(3*(cos(Lattice parameter alpha)^2))+(2*(cos(Lattice parameter alpha)^3))). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Volume?

Here are the different ways to Calculate Volume-

Volume=Edge Length^3
Volume=(2*Radius of Constituent Particle)^3
Volume=(4*Radius of Constituent Particle/sqrt(3))^3

Can the Volume of Rhombohedral cell be negative?

No, the Volume of Rhombohedral cell, measured in Volume cannot be negative.

Which unit is used to measure Volume of Rhombohedral cell?

Volume of Rhombohedral cell 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 Rhombohedral cell can be measured.

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