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Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Formula

GoSurface to Volume Ratio of Parallelepiped Formula

GoSurface to Volume Ratio of Parallelepiped given Volume, Side A and Side C Formula

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Surface to Volume Ratio of Parallelepiped is the numerical ratio of the total surface area of Parallelepiped to the volume of the Parallelepiped. Check FAQs

R A/V = \frac{LSA + 2 \cdot S a \cdot S c \cdot \sin (∠β)}{\frac{LSA \cdot S a \cdot S c}{2 \cdot (S a \cdot \sin (∠γ) + S c \cdot \sin (∠α))} \cdot \sqrt{1 + (2 \cdot \cos (∠α) \cdot \cos (∠β) \cdot \cos (∠γ)) - ({\cos (∠α)}^{2} + {\cos (∠β)}^{2} + {\cos (∠γ)}^{2})}}

R_A/V - Surface to Volume Ratio of Parallelepiped?LSA - Lateral Surface Area of Parallelepiped?S_a - Side A of Parallelepiped?S_c - Side C of Parallelepiped?∠β - Angle Beta of Parallelepiped?∠γ - Angle Gamma of Parallelepiped?∠α - Angle Alpha of Parallelepiped?

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Example

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

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

Here is how the Surface to Volume Ratio of Parallelepiped given Lateral Surface Area equation looks like.

0.5406 = \frac{1440 + 2 \cdot 30 \cdot 10 \cdot \sin (60)}{\frac{1440 \cdot 30 \cdot 10}{2 \cdot (30 \cdot \sin (75) + 10 \cdot \sin (45))} \cdot \sqrt{1 + (2 \cdot \cos (45) \cdot \cos (60) \cdot \cos (75)) - ({\cos (45)}^{2} + {\cos (60)}^{2} + {\cos (75)}^{2})}}

0.5406m⁻¹ = \frac{1440m² + 2 \cdot 30m \cdot 10m \cdot \sin (60°)}{\frac{1440m² \cdot 30m \cdot 10m}{2 \cdot (30m \cdot \sin (75°) + 10m \cdot \sin (45°))} \cdot \sqrt{1 + (2 \cdot \cos (45°) \cdot \cos (60°) \cdot \cos (75°)) - ({\cos (45°)}^{2} + {\cos (60°)}^{2} + {\cos (75°)}^{2})}}

0.5406 = \frac{1440 + 2 \cdot 30 \cdot 10 \cdot \sin (60)}{\frac{1440 \cdot 30 \cdot 10}{2 \cdot (30 \cdot \sin (75) + 10 \cdot \sin (45))} \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 Surface to Volume Ratio of Parallelepiped given Lateral Surface Area

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Solution

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

FIRST Step Consider the formula

R A/V = \frac{LSA + 2 \cdot S a \cdot S c \cdot \sin (∠β)}{\frac{LSA \cdot S a \cdot S c}{2 \cdot (S a \cdot \sin (∠γ) + S c \cdot \sin (∠α))} \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

∴

R A/V = \frac{1440m² + 2 \cdot 30m \cdot 10m \cdot \sin (60°)}{\frac{1440m² \cdot 30m \cdot 10m}{2 \cdot (30m \cdot \sin (75°) + 10m \cdot \sin (45°))} \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

∴

R A/V = \frac{1440m² + 2 \cdot 30m \cdot 10m \cdot \sin (1.0472rad)}{\frac{1440m² \cdot 30m \cdot 10m}{2 \cdot (30m \cdot \sin (1.309rad) + 10m \cdot \sin (0.7854rad))} \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

∴

R A/V = \frac{1440 + 2 \cdot 30 \cdot 10 \cdot \sin (1.0472)}{\frac{1440 \cdot 30 \cdot 10}{2 \cdot (30 \cdot \sin (1.309) + 10 \cdot \sin (0.7854))} \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

∴

R A/V = 0.54057103199881m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.5406m⁻¹

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Formula Elements

Variables

Functions

Surface to Volume Ratio of Parallelepiped

Surface to Volume Ratio of Parallelepiped is the numerical ratio of the total surface area of Parallelepiped to the volume of the Parallelepiped.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio 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 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 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 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

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

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 Surface to Volume Ratio of Parallelepiped

Go Surface to Volume Ratio of Parallelepiped

R A/V = \frac{2 \cdot ((S a \cdot S b \cdot \sin (∠γ)) + (S a \cdot S c \cdot \sin (∠β)) + (S b \cdot S c \cdot \sin (∠α)))}{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 Surface to Volume Ratio of Parallelepiped given Volume, Side A and Side C

R A/V = \frac{2 \cdot (\frac{V \cdot \sin (∠γ)}{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 a \cdot S c \cdot \sin (∠β)) + \frac{V \cdot \sin (∠α)}{S a \cdot \sqrt{1 + (2 \cdot \cos (∠α) \cdot \cos (∠β) \cdot \cos (∠γ)) - ({\cos (∠α)}^{2} + {\cos (∠β)}^{2} + {\cos (∠γ)}^{2})}})}{V}

How to Evaluate Surface to Volume Ratio of Parallelepiped given Lateral Surface Area?

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area evaluator uses Surface to Volume Ratio of Parallelepiped = (Lateral Surface Area of Parallelepiped+2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta 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))) to evaluate the Surface to Volume Ratio of Parallelepiped, The Surface to Volume Ratio of Parallelepiped given Lateral Surface Area formula is defined as the numerical ratio of the total surface area of Parallelepiped to the volume of the Parallelepiped, calculated using lateral surface area of Parallelepiped. Surface to Volume Ratio of Parallelepiped is denoted by R_A/V symbol.

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

FAQs on Surface to Volume Ratio of Parallelepiped given Lateral Surface Area

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

The formula of Surface to Volume Ratio of Parallelepiped given Lateral Surface Area is expressed as Surface to Volume Ratio of Parallelepiped = (Lateral Surface Area of Parallelepiped+2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta 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))). Here is an example- 0.540571 = (1440+2*30*10*sin(1.0471975511964))/((1440*30*10)/(2*(30*sin(1.3089969389955)+10*sin(0.785398163397301)))*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 Surface to Volume Ratio of Parallelepiped given Lateral Surface Area?

With Lateral Surface Area of Parallelepiped (LSA), Side A of Parallelepiped (S_a), Side C of Parallelepiped (S_c), Angle Beta of Parallelepiped (∠β), Angle Gamma of Parallelepiped (∠γ) & Angle Alpha of Parallelepiped (∠α) we can find Surface to Volume Ratio of Parallelepiped given Lateral Surface Area using the formula - Surface to Volume Ratio of Parallelepiped = (Lateral Surface Area of Parallelepiped+2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta 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))). This formula also uses Sine (sin)Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Surface to Volume Ratio of Parallelepiped?

Here are the different ways to Calculate Surface to Volume Ratio of Parallelepiped-

Surface to Volume Ratio of Parallelepiped=(2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha 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)))
Surface to Volume Ratio of Parallelepiped=(2*((Volume of Parallelepiped*sin(Angle Gamma 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)))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Volume of Parallelepiped*sin(Angle Alpha of Parallelepiped))/(Side A 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
Surface to Volume Ratio of Parallelepiped=(2*((Volume of Parallelepiped*sin(Angle Gamma 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*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)))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))))/Volume of Parallelepiped

Can the Surface to Volume Ratio of Parallelepiped given Lateral Surface Area be negative?

No, the Surface to Volume Ratio of Parallelepiped given Lateral Surface Area, measured in Reciprocal Length cannot be negative.

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

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Surface to Volume Ratio of Parallelepiped given Lateral Surface Area can be measured.

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Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Formula

​GoSurface to Volume Ratio of Parallelepiped Formula

​GoSurface to Volume Ratio of Parallelepiped given Volume, Side A and Side C Formula

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Example

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Solution

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Formula Elements

Other Formulas to find Surface to Volume Ratio of Parallelepiped

How to Evaluate Surface to Volume Ratio of Parallelepiped given Lateral Surface Area?

FAQs on Surface to Volume Ratio of Parallelepiped given Lateral Surface Area

Variable Name

GoSurface to Volume Ratio of Parallelepiped Formula

GoSurface to Volume Ratio of Parallelepiped given Volume, Side A and Side C Formula