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Volume of Parallelepiped given Perimeter, Side A and Side B Formula

GoVolume 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 (\frac{P}{4} - S a - S b) \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?P - Perimeter of Parallelepiped?∠α - Angle Alpha of Parallelepiped?∠β - Angle Beta of Parallelepiped?∠γ - Angle Gamma of Parallelepiped?

Volume of Parallelepiped given Perimeter, Side A and Side B Example

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Here is how the Volume of Parallelepiped given Perimeter, Side A and Side B equation looks like with Values.

Here is how the Volume of Parallelepiped given Perimeter, Side A and Side B equation looks like with Units.

Here is how the Volume of Parallelepiped given Perimeter, Side A and Side B equation looks like.

3630.002 = 30 \cdot 20 \cdot (\frac{240}{4} - 30 - 20) \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 (\frac{240m}{4} - 30m - 20m) \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 (\frac{240}{4} - 30 - 20) \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 given Perimeter, Side A and Side B Solution

Follow our step by step solution on how to calculate Volume of Parallelepiped given Perimeter, Side A and Side B?

FIRST Step Consider the formula

V = S a \cdot S b \cdot (\frac{P}{4} - S a - S b) \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 (\frac{240m}{4} - 30m - 20m) \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 (\frac{240m}{4} - 30m - 20m) \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 (\frac{240}{4} - 30 - 20) \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 given Perimeter, Side A and Side B 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

Perimeter of Parallelepiped

Perimeter of Parallelepiped is the total distance around the edge of the Parallelepiped.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter 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

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})}

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 given Perimeter, Side A and Side B?

Volume of Parallelepiped given Perimeter, Side A and Side B evaluator uses Volume of Parallelepiped = Side A of Parallelepiped*Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A 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)) to evaluate the Volume of Parallelepiped, The Volume of Parallelepiped given Perimeter, Side A and Side B formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped, calculated using perimeter, side A and side B of Parallelepiped. Volume of Parallelepiped is denoted by V symbol.

How to evaluate Volume of Parallelepiped given Perimeter, Side A and Side B using this online evaluator? To use this online evaluator for Volume of Parallelepiped given Perimeter, Side A and Side B, enter Side A of Parallelepiped (S_a), Side B of Parallelepiped (S_b), Perimeter of Parallelepiped (P), 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 given Perimeter, Side A and Side B

What is the formula to find Volume of Parallelepiped given Perimeter, Side A and Side B?

The formula of Volume of Parallelepiped given Perimeter, Side A and Side B is expressed as Volume of Parallelepiped = Side A of Parallelepiped*Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A 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)). Here is an example- 3630.002 = 30*20*(240/4-30-20)*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 given Perimeter, Side A and Side B?

With Side A of Parallelepiped (S_a), Side B of Parallelepiped (S_b), Perimeter of Parallelepiped (P), Angle Alpha of Parallelepiped (∠α), Angle Beta of Parallelepiped (∠β) & Angle Gamma of Parallelepiped (∠γ) we can find Volume of Parallelepiped given Perimeter, Side A and Side B using the formula - Volume of Parallelepiped = Side A of Parallelepiped*Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A 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)). This formula also uses Cosine (cos), Square Root (sqrt) 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=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))
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))
Volume of Parallelepiped=(Lateral Surface Area of Parallelepiped*Side A of Parallelepiped*Side C of Parallelepiped)/(2*(Side A of Parallelepiped*sin(Angle Gamma of Parallelepiped)+Side C of Parallelepiped*sin(Angle Alpha 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 given Perimeter, Side A and Side B be negative?

No, the Volume of Parallelepiped given Perimeter, Side A and Side B, measured in Volume cannot be negative.

Which unit is used to measure Volume of Parallelepiped given Perimeter, Side A and Side B?

Volume of Parallelepiped given Perimeter, Side A and Side B 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 given Perimeter, Side A and Side B can be measured.

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Volume of Parallelepiped given Perimeter, Side A and Side B Formula

​GoVolume of Parallelepiped Formula

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

Volume of Parallelepiped given Perimeter, Side A and Side B Example

Volume of Parallelepiped given Perimeter, Side A and Side B Solution

Volume of Parallelepiped given Perimeter, Side A and Side B Formula Elements

Other Formulas to find Volume of Parallelepiped

How to Evaluate Volume of Parallelepiped given Perimeter, Side A and Side B?

FAQs on Volume of Parallelepiped given Perimeter, Side A and Side B

Variable Name

GoVolume of Parallelepiped Formula

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