Surface to Volume Ratio of Parallelepiped Calculator

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Parallelepiped	Surface to Volume Ratio of Parallelepiped ↺

✖Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.ⓘ Side A of Parallelepiped [S_a]			+10% -10%
✖Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.ⓘ Side B of Parallelepiped [S_b]			+10% -10%
✖Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped.ⓘ Angle Gamma of Parallelepiped [∠γ]			+10% -10%
✖Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.ⓘ Side C of Parallelepiped [S_c]			+10% -10%
✖Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.ⓘ Angle Beta of Parallelepiped [∠β]			+10% -10%
✖Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.ⓘ Angle Alpha of Parallelepiped [∠α]			+10% -10%

✖Surface to Volume Ratio of Parallelepiped is the numerical ratio of the total surface area of Parallelepiped to the volume of the Parallelepiped.ⓘ Surface to Volume Ratio of Parallelepiped [R_A/V]

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Formula

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Surface to Volume Ratio of Parallelepiped

Formula

`"R"_{"A/V"} = (2*(("S"_{"a"}*"S"_{"b"}*sin("∠γ"))+("S"_{"a"}*"S"_{"c"}*sin("∠β"))+("S"_{"b"}*"S"_{"c"}*sin("∠α"))))/("S"_{"a"}*"S"_{"b"}*"S"_{"c"}*sqrt(1+(2*cos("∠α")*cos("∠β")*cos("∠γ"))-(cos("∠α")^2+cos("∠β")^2+cos("∠γ")^2)))`

Example

`"0.540377m⁻¹"=(2*(("30m"*"20m"*sin("75°"))+("30m"*"10m"*sin("60°"))+("20m"*"10m"*sin("45°"))))/("30m"*"20m"*"10m"*sqrt(1+(2*cos("45°")*cos("60°")*cos("75°"))-(cos("45°")^2+cos("60°")^2+cos("75°")^2)))`

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Surface to Volume Ratio of Parallelepiped Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
R_A/V = (2*((S_a*S_b*sin(∠γ))+(S_a*S_c*sin(∠β))+(S_b*S_c*sin(∠α))))/(S_a*S_b*S_c*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2)))
This formula uses 3 Functions, 7 Variables

Functions Used

sin - Trigonometric sine function, sin(Angle)
cos - Trigonometric cosine function, cos(Angle)
sqrt - Square root function, sqrt(Number)

Variables Used

Surface to Volume Ratio of Parallelepiped - (Measured in 1 per Meter) - Surface to Volume Ratio of Parallelepiped is the numerical ratio of the total surface area of Parallelepiped to the volume of the Parallelepiped.
Side A of Parallelepiped - (Measured in Meter) - Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.
Side B of Parallelepiped - (Measured in Meter) - Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.
Angle Gamma of Parallelepiped - (Measured in Radian) - Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped.
Side C of Parallelepiped - (Measured in Meter) - Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.
Angle Beta of Parallelepiped - (Measured in Radian) - Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.
Angle Alpha of Parallelepiped - (Measured in Radian) - Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.

STEP 1: Convert Input(s) to Base Unit

Side A of Parallelepiped: 30 Meter --> 30 Meter No Conversion Required
Side B of Parallelepiped: 20 Meter --> 20 Meter No Conversion Required
Angle Gamma of Parallelepiped: 75 Degree --> 1.3089969389955 Radian (Check conversion here)
Side C of Parallelepiped: 10 Meter --> 10 Meter No Conversion Required
Angle Beta of Parallelepiped: 60 Degree --> 1.0471975511964 Radian (Check conversion here)
Angle Alpha of Parallelepiped: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (2*((S_a*S_b*sin(∠γ))+(S_a*S_c*sin(∠β))+(S_b*S_c*sin(∠α))))/(S_a*S_b*S_c*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2))) --> (2*((30*20*sin(1.3089969389955))+(30*10*sin(1.0471975511964))+(20*10*sin(0.785398163397301))))/(30*20*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)))

Evaluating ... ...

R_A/V = 0.540376822129579

STEP 3: Convert Result to Output's Unit

0.540376822129579 1 per Meter --> No Conversion Required

FINAL ANSWER

0.540376822129579 ≈ 0.540377 1 per Meter <-- Surface to Volume Ratio of Parallelepiped

(Calculation completed in 00.007 seconds)

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< 1 Surface to Volume Ratio of Parallelepiped Calculators

Surface to Volume Ratio of Parallelepiped

Go 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 Formula

What is Parallelepiped?

A Parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. In Euclidean geometry, the four concepts—parallelepiped and cube in three dimensions, parallelogram and square in two dimensions—are defined, but in the context of a more general affine geometry, in which angles are not differentiated, only parallelograms and parallelepipeds exist.

How to Calculate Surface to Volume Ratio of Parallelepiped?

Surface to Volume Ratio of Parallelepiped calculator uses 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))) to calculate the Surface to Volume Ratio of Parallelepiped, The Surface to Volume Ratio of Parallelepiped formula is defined as the numerical ratio of the total surface area of Parallelepiped to the volume of the Parallelepiped. Surface to Volume Ratio of Parallelepiped is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Parallelepiped using this online calculator? To use this online calculator for Surface to Volume Ratio of Parallelepiped, enter Side A of Parallelepiped (S_a), Side B of Parallelepiped (S_b), Angle Gamma of Parallelepiped (∠γ), Side C of Parallelepiped (S_c), Angle Beta of Parallelepiped (∠β) & Angle Alpha of Parallelepiped (∠α) and hit the calculate button. Here is how the Surface to Volume Ratio of Parallelepiped calculation can be explained with given input values -> 0.540377 = (2*((30*20*sin(1.3089969389955))+(30*10*sin(1.0471975511964))+(20*10*sin(0.785398163397301))))/(30*20*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))).

FAQ

What is Surface to Volume Ratio of Parallelepiped?

The Surface to Volume Ratio of Parallelepiped formula is defined as the numerical ratio of the total surface area of Parallelepiped to the volume of the Parallelepiped and is represented as R_A/V = (2*((S_a*S_b*sin(∠γ))+(S_a*S_c*sin(∠β))+(S_b*S_c*sin(∠α))))/(S_a*S_b*S_c*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2))) or 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))). Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped, Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the 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, Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the 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 & Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.

How to calculate Surface to Volume Ratio of Parallelepiped?

The Surface to Volume Ratio of Parallelepiped formula is defined as the numerical ratio of the total surface area of Parallelepiped to the volume of the Parallelepiped is calculated using 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))). To calculate Surface to Volume Ratio of Parallelepiped, you need Side A of Parallelepiped (S_a), Side B of Parallelepiped (S_b), Angle Gamma of Parallelepiped (∠γ), Side C of Parallelepiped (S_c), Angle Beta of Parallelepiped (∠β) & Angle Alpha of Parallelepiped (∠α). With our tool, you need to enter the respective value for Side A of Parallelepiped, Side B of Parallelepiped, Angle Gamma of Parallelepiped, Side C of Parallelepiped, Angle Beta of Parallelepiped & Angle Alpha of Parallelepiped and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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