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Volume of Parallelepiped Formula

GoVolume of Parallelepiped given Total Surface Area and Lateral Surface Area Formula

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

V = S a \cdot S b \cdot S c \cdot \sqrt{1 + (2 \cdot \cos (∠α) \cdot \cos (∠β) \cdot \cos (∠γ)) - ({\cos (∠α)}^{2} + {\cos (∠β)}^{2} + {\cos (∠γ)}^{2})}

V - Volume of Parallelepiped?S_a - Side A of Parallelepiped?S_b - Side B of Parallelepiped?S_c - Side C of Parallelepiped?∠α - Angle Alpha of Parallelepiped?∠β - Angle Beta of Parallelepiped?∠γ - Angle Gamma of Parallelepiped?

Volume of Parallelepiped Example

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

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

Here is how the Volume of Parallelepiped equation looks like.

3630.002 = 30 \cdot 20 \cdot 10 \cdot \sqrt{1 + (2 \cdot \cos (45) \cdot \cos (60) \cdot \cos (75)) - ({\cos (45)}^{2} + {\cos (60)}^{2} + {\cos (75)}^{2})}

3630.002m³ = 30m \cdot 20m \cdot 10m \cdot \sqrt{1 + (2 \cdot \cos (45°) \cdot \cos (60°) \cdot \cos (75°)) - ({\cos (45°)}^{2} + {\cos (60°)}^{2} + {\cos (75°)}^{2})}

3630.002 = 30 \cdot 20 \cdot 10 \cdot \sqrt{1 + (2 \cdot \cos (45) \cdot \cos (60) \cdot \cos (75)) - ({\cos (45)}^{2} + {\cos (60)}^{2} + {\cos (75)}^{2})}

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Volume of Parallelepiped Solution

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

FIRST Step Consider the formula

V = S a \cdot S b \cdot S c \cdot \sqrt{1 + (2 \cdot \cos (∠α) \cdot \cos (∠β) \cdot \cos (∠γ)) - ({\cos (∠α)}^{2} + {\cos (∠β)}^{2} + {\cos (∠γ)}^{2})}

Next Step Substitute values of Variables

∴

V = 30m \cdot 20m \cdot 10m \cdot \sqrt{1 + (2 \cdot \cos (45°) \cdot \cos (60°) \cdot \cos (75°)) - ({\cos (45°)}^{2} + {\cos (60°)}^{2} + {\cos (75°)}^{2})}

Next Step Convert Units

∴

V = 30m \cdot 20m \cdot 10m \cdot \sqrt{1 + (2 \cdot \cos (0.7854rad) \cdot \cos (1.0472rad) \cdot \cos (1.309rad)) - ({\cos (0.7854rad)}^{2} + {\cos (1.0472rad)}^{2} + {\cos (1.309rad)}^{2})}

Next Step Prepare to Evaluate

∴

V = 30 \cdot 20 \cdot 10 \cdot \sqrt{1 + (2 \cdot \cos (0.7854) \cdot \cos (1.0472) \cdot \cos (1.309)) - ({\cos (0.7854)}^{2} + {\cos (1.0472)}^{2} + {\cos (1.309)}^{2})}

Next Step Evaluate

∴

V = 3630.00200223542m³

LAST Step Rounding Answer

∴

V = 3630.002m³

Volume of Parallelepiped Formula Elements

Variables

Functions

Volume of Parallelepiped

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Parallelepiped

Side A of Parallelepiped

Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Parallelepiped

Side B of Parallelepiped

Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Parallelepiped

Side C of Parallelepiped

Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Parallelepiped

Angle Alpha of Parallelepiped

Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.

Symbol: ∠α

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Alpha of Parallelepiped

Angle Beta of Parallelepiped

Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.

Symbol: ∠β

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Beta of Parallelepiped

Angle Gamma of Parallelepiped

Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped.

Symbol: ∠γ

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Gamma of Parallelepiped

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 Parallelepiped

Go Volume of Parallelepiped given Total Surface Area and Lateral Surface Area

V = \frac{1}{2} \cdot \frac{TSA - LSA}{\sin (∠β)} \cdot S b \cdot \sqrt{1 + (2 \cdot \cos (∠α) \cdot \cos (∠β) \cdot \cos (∠γ)) - ({\cos (∠α)}^{2} + {\cos (∠β)}^{2} + {\cos (∠γ)}^{2})}

How to Evaluate Volume of Parallelepiped?

Volume of Parallelepiped evaluator uses Volume of Parallelepiped = Side A of Parallelepiped*Side B of Parallelepiped*Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)) to evaluate the Volume of Parallelepiped, The Volume of Parallelepiped formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped. Volume of Parallelepiped is denoted by V symbol.

How to evaluate Volume of Parallelepiped using this online evaluator? To use this online evaluator for Volume of Parallelepiped, enter Side A of Parallelepiped (S_a), Side B of Parallelepiped (S_b), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α), Angle Beta of Parallelepiped (∠β) & Angle Gamma of Parallelepiped (∠γ) and hit the calculate button.

FAQs on Volume of Parallelepiped

What is the formula to find Volume of Parallelepiped?

The formula of Volume of Parallelepiped is expressed as Volume of Parallelepiped = Side A of Parallelepiped*Side B of Parallelepiped*Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)). Here is an example- 3630.002 = 30*20*10*sqrt(1+(2*cos(0.785398163397301)*cos(1.0471975511964)*cos(1.3089969389955))-(cos(0.785398163397301)^2+cos(1.0471975511964)^2+cos(1.3089969389955)^2)).

How to calculate Volume of Parallelepiped?

With Side A of Parallelepiped (S_a), Side B of Parallelepiped (S_b), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α), Angle Beta of Parallelepiped (∠β) & Angle Gamma of Parallelepiped (∠γ) we can find Volume of Parallelepiped using the formula - Volume of Parallelepiped = Side A of Parallelepiped*Side B of Parallelepiped*Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)). This formula also uses Cosine, Square Root Function function(s).

What are the other ways to Calculate Volume of Parallelepiped?

Here are the different ways to Calculate Volume of Parallelepiped-

Volume of Parallelepiped=1/2*(Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/sin(Angle Beta of Parallelepiped)*Side B of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2))

Can the Volume of Parallelepiped be negative?

No, the Volume of Parallelepiped, measured in Volume cannot be negative.

Which unit is used to measure Volume of Parallelepiped?

Volume of Parallelepiped 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 Parallelepiped can be measured.

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Volume of Parallelepiped Formula

​GoVolume of Parallelepiped given Total Surface Area and Lateral Surface Area Formula

Volume of Parallelepiped Example

Volume of Parallelepiped Solution

Volume of Parallelepiped Formula Elements

Other Formulas to find Volume of Parallelepiped

How to Evaluate Volume of Parallelepiped?

FAQs on Volume of Parallelepiped

Variable Name

GoVolume of Parallelepiped given Total Surface Area and Lateral Surface Area Formula