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Volume of Parallelepiped given Lateral Surface Area, 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 = \frac{S a}{\sin (∠α)} \cdot (\frac{LSA}{2} - S a \cdot S b \cdot \sin (∠γ)) \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?∠α - Angle Alpha of Parallelepiped?LSA - Lateral Surface Area of Parallelepiped?S_b - Side B of Parallelepiped?∠γ - Angle Gamma of Parallelepiped?∠β - Angle Beta of Parallelepiped?

Volume of Parallelepiped given Lateral Surface Area, Side A and Side B Example

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

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

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

3604.9282 = \frac{30}{\sin (45)} \cdot (\frac{1440}{2} - 30 \cdot 20 \cdot \sin (75)) \cdot \sqrt{1 + (2 \cdot \cos (45) \cdot \cos (60) \cdot \cos (75)) - ({\cos (45)}^{2} + {\cos (60)}^{2} + {\cos (75)}^{2})}

3604.9282m³ = \frac{30m}{\sin (45°)} \cdot (\frac{1440m²}{2} - 30m \cdot 20m \cdot \sin (75°)) \cdot \sqrt{1 + (2 \cdot \cos (45°) \cdot \cos (60°) \cdot \cos (75°)) - ({\cos (45°)}^{2} + {\cos (60°)}^{2} + {\cos (75°)}^{2})}

3604.9282 = \frac{30}{\sin (45)} \cdot (\frac{1440}{2} - 30 \cdot 20 \cdot \sin (75)) \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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3D Geometry » fx Volume of Parallelepiped given Lateral Surface Area, Side A and Side B

Volume of Parallelepiped given Lateral Surface Area, Side A and Side B Solution

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

FIRST Step Consider the formula

V = \frac{S a}{\sin (∠α)} \cdot (\frac{LSA}{2} - S a \cdot S b \cdot \sin (∠γ)) \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 = \frac{30m}{\sin (45°)} \cdot (\frac{1440m²}{2} - 30m \cdot 20m \cdot \sin (75°)) \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 = \frac{30m}{\sin (0.7854rad)} \cdot (\frac{1440m²}{2} - 30m \cdot 20m \cdot \sin (1.309rad)) \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 = \frac{30}{\sin (0.7854)} \cdot (\frac{1440}{2} - 30 \cdot 20 \cdot \sin (1.309)) \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 = 3604.92817428579m³

LAST Step Rounding Answer

∴

V = 3604.9282m³

Volume of Parallelepiped given Lateral Surface Area, 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

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

Lateral Surface Area of Parallelepiped

Lateral Surface Area of Parallelepiped is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area 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

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

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

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 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 Lateral Surface Area, Side A and Side B?

Volume of Parallelepiped given Lateral Surface Area, Side A and Side B evaluator uses Volume of Parallelepiped = Side A of Parallelepiped/sin(Angle Alpha of Parallelepiped)*(Lateral Surface Area of Parallelepiped/2-Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma 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 Lateral Surface Area, Side A and Side B formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped, calculated using lateral surface area, side A and side B of Parallelepiped. Volume of Parallelepiped is denoted by V symbol.

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

FAQs on Volume of Parallelepiped given Lateral Surface Area, Side A and Side B

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

The formula of Volume of Parallelepiped given Lateral Surface Area, Side A and Side B is expressed as Volume of Parallelepiped = Side A of Parallelepiped/sin(Angle Alpha of Parallelepiped)*(Lateral Surface Area of Parallelepiped/2-Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma 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- 3604.928 = 30/sin(0.785398163397301)*(1440/2-30*20*sin(1.3089969389955))*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 Lateral Surface Area, Side A and Side B?

With Side A of Parallelepiped (S_a), Angle Alpha of Parallelepiped (∠α), Lateral Surface Area of Parallelepiped (LSA), Side B of Parallelepiped (S_b), Angle Gamma of Parallelepiped (∠γ) & Angle Beta of Parallelepiped (∠β) we can find Volume of Parallelepiped given Lateral Surface Area, Side A and Side B using the formula - Volume of Parallelepiped = Side A of Parallelepiped/sin(Angle Alpha of Parallelepiped)*(Lateral Surface Area of Parallelepiped/2-Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma 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 SineCosine, 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=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 Lateral Surface Area, Side A and Side B be negative?

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

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

Volume of Parallelepiped given Lateral Surface Area, 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 Lateral Surface Area, Side A and Side B can be measured.

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Volume of Parallelepiped given Lateral Surface Area, 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 Lateral Surface Area, Side A and Side B Example

Volume of Parallelepiped given Lateral Surface Area, Side A and Side B Solution

Volume of Parallelepiped given Lateral Surface Area, Side A and Side B Formula Elements

Other Formulas to find Volume of Parallelepiped

How to Evaluate Volume of Parallelepiped given Lateral Surface Area, Side A and Side B?

FAQs on Volume of Parallelepiped given Lateral Surface Area, Side A and Side B

Variable Name

GoVolume of Parallelepiped Formula

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