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Side B of Parallelepiped Formula

GoSide B of Parallelepiped given Lateral Surface Area Formula

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

S b = \frac{V}{S a \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})}}

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

Side B of Parallelepiped Example

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With units

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

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

Here is how the Side B of Parallelepiped equation looks like.

20 = \frac{3630}{30 \cdot 10 \cdot \sqrt{1 + (2 \cdot \cos (45) \cdot \cos (60) \cdot \cos (75)) - ({\cos (45)}^{2} + {\cos (60)}^{2} + {\cos (75)}^{2})}}

20m = \frac{3630m³}{30m \cdot 10m \cdot \sqrt{1 + (2 \cdot \cos (45°) \cdot \cos (60°) \cdot \cos (75°)) - ({\cos (45°)}^{2} + {\cos (60°)}^{2} + {\cos (75°)}^{2})}}

20 = \frac{3630}{30 \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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Home » Math » Geometry » 3D Geometry » Side B of Parallelepiped

Side B of Parallelepiped Solution

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

FIRST Step Consider the formula

S b = \frac{V}{S a \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

∴

S b = \frac{3630m³}{30m \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

∴

S b = \frac{3630m³}{30m \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

∴

S b = \frac{3630}{30 \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

∴

S b = 19.999988968406m

LAST Step Rounding Answer

∴

S b = 20m

Side B of Parallelepiped Formula Elements

Variables

Functions

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.

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.

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.

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.

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 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.

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.

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 Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Formula and 2000+ more formulas!

Verified by

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Formula and 1700+ more formulas!

Other Formulas to find Side B of Parallelepiped

Go Side B of Parallelepiped given Lateral Surface Area

S b = \frac{LSA}{2 \cdot (S a \cdot \sin (∠γ) + S c \cdot \sin (∠α))}

Other formulas in Side of Parallelepiped category

Go Side A of Parallelepiped

S a = \frac{V}{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 Side C of Parallelepiped

S c = \frac{V}{S b \cdot S a \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 Side B of Parallelepiped?

Side B of Parallelepiped evaluator uses Side B of Parallelepiped = Volume of Parallelepiped/(Side A 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 Side B of Parallelepiped, Side B of Parallelepiped formula is defined as the length of any one out of the three sides from any fixed vertex of the Parallelepiped. Side B of Parallelepiped is denoted by S_b symbol.

How to evaluate Side B of Parallelepiped using this online evaluator? To use this online evaluator for Side B of Parallelepiped, enter Volume of Parallelepiped (V), Side A of Parallelepiped (S_a), 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 Side B of Parallelepiped

What is the formula to find Side B of Parallelepiped?

The formula of Side B of Parallelepiped is expressed as Side B of Parallelepiped = Volume of Parallelepiped/(Side A 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- 19.99999 = 3630/(30*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 Side B of Parallelepiped?

With Volume of Parallelepiped (V), Side A of Parallelepiped (S_a), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α), Angle Beta of Parallelepiped (∠β) & Angle Gamma of Parallelepiped (∠γ) we can find Side B of Parallelepiped using the formula - Side B of Parallelepiped = Volume of Parallelepiped/(Side A 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 (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Side B of Parallelepiped?

Here are the different ways to Calculate Side B of Parallelepiped-

Side B of Parallelepiped=Lateral Surface Area of Parallelepiped/(2*(Side A of Parallelepiped*sin(Angle Gamma of Parallelepiped)+Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))

Can the Side B of Parallelepiped be negative?

No, the Side B of Parallelepiped, measured in Length cannot be negative.

Which unit is used to measure Side B of Parallelepiped?

Side B of Parallelepiped is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Side B of Parallelepiped can be measured.