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

GoVolume of Parallelepiped 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{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})}

V - Volume of Parallelepiped?TSA - Total Surface Area of Parallelepiped?LSA - Lateral Surface Area of Parallelepiped?∠β - Angle Beta of Parallelepiped?S_b - Side B of Parallelepiped?∠α - Angle Alpha of Parallelepiped?∠γ - Angle Gamma of Parallelepiped?

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

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Here is how the Volume of Parallelepiped given Total Surface Area and Lateral Surface Area equation looks like with Values.

Here is how the Volume of Parallelepiped given Total Surface Area and Lateral Surface Area equation looks like with Units.

Here is how the Volume of Parallelepiped given Total Surface Area and Lateral Surface Area equation looks like.

3632.6899 = \frac{1}{2} \cdot \frac{1960 - 1440}{\sin (60)} \cdot 20 \cdot \sqrt{1 + (2 \cdot \cos (45) \cdot \cos (60) \cdot \cos (75)) - ({\cos (45)}^{2} + {\cos (60)}^{2} + {\cos (75)}^{2})}

3632.6899m³ = \frac{1}{2} \cdot \frac{1960m² - 1440m²}{\sin (60°)} \cdot 20m \cdot \sqrt{1 + (2 \cdot \cos (45°) \cdot \cos (60°) \cdot \cos (75°)) - ({\cos (45°)}^{2} + {\cos (60°)}^{2} + {\cos (75°)}^{2})}

3632.6899 = \frac{1}{2} \cdot \frac{1960 - 1440}{\sin (60)} \cdot 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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Home » Math » Geometry » 3D Geometry » Volume of Parallelepiped given Total Surface Area and Lateral Surface Area

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

Follow our step by step solution on how to calculate Volume of Parallelepiped given Total Surface Area and Lateral Surface Area?

FIRST Step Consider the formula

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})}

Next Step Substitute values of Variables

∴

V = \frac{1}{2} \cdot \frac{1960m² - 1440m²}{\sin (60°)} \cdot 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 = \frac{1}{2} \cdot \frac{1960m² - 1440m²}{\sin (1.0472rad)} \cdot 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 = \frac{1}{2} \cdot \frac{1960 - 1440}{\sin (1.0472)} \cdot 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 = 3632.68989745955m³

LAST Step Rounding Answer

∴

V = 3632.6899m³

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

Total Surface Area of Parallelepiped

Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

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.

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.

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.

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.

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.

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)

Credits

Created by Diwanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

Diwanshi Jain has created this Formula and 300+ more formulas!

Verified by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has verified this Formula and 400+ more formulas!

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})}

How to Evaluate Volume of Parallelepiped given Total Surface Area and Lateral Surface Area?

Volume of Parallelepiped given Total Surface Area and Lateral Surface Area evaluator uses 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)) to evaluate the Volume of Parallelepiped, The Volume of Parallelepiped given Total Surface Area and Lateral Surface Area formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped, calculated using total surface area and lateral surface area of Parallelepiped. Volume of Parallelepiped is denoted by V symbol.

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

FAQs on Volume of Parallelepiped given Total Surface Area and Lateral Surface Area

What is the formula to find Volume of Parallelepiped given Total Surface Area and Lateral Surface Area?

The formula of Volume of Parallelepiped given Total Surface Area and Lateral Surface Area is expressed as 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)). Here is an example- 3632.69 = 1/2*(1960-1440)/sin(1.0471975511964)*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 Total Surface Area and Lateral Surface Area?

With Total Surface Area of Parallelepiped (TSA), Lateral Surface Area of Parallelepiped (LSA), Angle Beta of Parallelepiped (∠β), Side B of Parallelepiped (S_b), Angle Alpha of Parallelepiped (∠α) & Angle Gamma of Parallelepiped (∠γ) we can find Volume of Parallelepiped given Total Surface Area and Lateral Surface Area using the formula - 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)). This formula also uses Sine (sin)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))

Can the Volume of Parallelepiped given Total Surface Area and Lateral Surface Area be negative?

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

Which unit is used to measure Volume of Parallelepiped given Total Surface Area and Lateral Surface Area?

Volume of Parallelepiped given Total Surface Area and Lateral Surface Area 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 Total Surface Area and Lateral Surface Area can be measured.

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

​GoVolume of Parallelepiped Formula

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

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

Volume of Parallelepiped given Total Surface Area and Lateral Surface Area Formula Elements

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Other Formulas to find Volume of Parallelepiped

How to Evaluate Volume of Parallelepiped given Total Surface Area and Lateral Surface Area?

FAQs on Volume of Parallelepiped given Total Surface Area and Lateral Surface Area

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GoVolume of Parallelepiped Formula