Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Calculator

✖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.ⓘ Lateral Surface Area of Parallelepiped [LSA]			+10% -10%
✖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 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 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%
✖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 given Lateral Surface Area [R_A/V]

⎘ Copy

👎

Formula

✖

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area

Formula

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

Example

`"0.540571m⁻¹"=("1440m²"+2*"30m"*"10m"*sin("60°"))/(("1440m²"*"30m"*"10m")/(2*("30m"*sin("75°")+"10m"*sin("45°")))*sqrt(1+(2*cos("45°")*cos("60°")*cos("75°"))-(cos("45°")^2+cos("60°")^2+cos("75°")^2)))`

Calculator

LaTeX

Reset

👍

Download Parallelepiped Formula PDF PDF Image

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
R_A/V = (LSA+2*S_a*S_c*sin(∠β))/((LSA*S_a*S_c)/(2*(S_a*sin(∠γ)+S_c*sin(∠α)))*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 - 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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., 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.
Lateral Surface Area of Parallelepiped - (Measured in Square Meter) - 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.
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 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 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.
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

Lateral Surface Area of Parallelepiped: 1440 Square Meter --> 1440 Square Meter No Conversion Required
Side A of Parallelepiped: 30 Meter --> 30 Meter No Conversion Required
Side C of Parallelepiped: 10 Meter --> 10 Meter No Conversion Required
Angle Beta of Parallelepiped: 60 Degree --> 1.0471975511964 Radian (Check conversion here)
Angle Gamma of Parallelepiped: 75 Degree --> 1.3089969389955 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 = (LSA+2*S_a*S_c*sin(∠β))/((LSA*S_a*S_c)/(2*(S_a*sin(∠γ)+S_c*sin(∠α)))*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2))) --> (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)))

Evaluating ... ...

R_A/V = 0.54057103199881

STEP 3: Convert Result to Output's Unit

0.54057103199881 1 per Meter --> No Conversion Required

FINAL ANSWER

0.54057103199881 ≈ 0.540571 1 per Meter <-- Surface to Volume Ratio of Parallelepiped

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Parallelepiped » Surface to Volume Ratio of Parallelepiped » Surface to Volume Ratio of Parallelepiped given Lateral Surface Area

Credits

Created by Divanshi Jain

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

Divanshi Jain has created this Calculator and 300+ more calculators!

Verified by Dhruv Walia

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

Dhruv Walia has verified this Calculator and 400+ more calculators!

< 8 Surface to Volume Ratio of Parallelepiped Calculators

Surface to Volume Ratio of Parallelepiped given Volume, Side A and Side C

Go 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 given Volume, Side B and Side C

Go 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

Surface to Volume Ratio of Parallelepiped given Volume, Side A and Side B

Go Surface to Volume Ratio of Parallelepiped = (2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(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)))+(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 given Perimeter, Side A and Side B

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*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped)*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped)*sin(Angle Alpha of Parallelepiped))))/(Side A of Parallelepiped*Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A 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)))

Surface to Volume Ratio of Parallelepiped given Perimeter, Side A and Side C

Go Surface to Volume Ratio of Parallelepiped = (2*((Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+((Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))))/(Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C 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 given Perimeter, Side B and Side C

Go Surface to Volume Ratio of Parallelepiped = (2*(((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped)*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))))/((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C 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

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 given Lateral Surface Area

Go 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)))

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Formula

What is a 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 given Lateral Surface Area?

Surface to Volume Ratio of Parallelepiped given Lateral Surface Area calculator 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 calculate 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 calculate Surface to Volume Ratio of Parallelepiped given Lateral Surface Area using this online calculator? To use this online calculator 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. Here is how the Surface to Volume Ratio of Parallelepiped given Lateral Surface Area calculation can be explained with given input values -> 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))).

FAQ

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

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 and is represented as R_A/V = (LSA+2*S_a*S_c*sin(∠β))/((LSA*S_a*S_c)/(2*(S_a*sin(∠γ)+S_c*sin(∠α)))*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 = (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))). 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, Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex 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 Gamma of Parallelepiped is the angle formed by side A and side B 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 given Lateral Surface Area?

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 is calculated using 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 calculate Surface to Volume Ratio of Parallelepiped given Lateral Surface Area, you need 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). With our tool, you need to enter the respective value for Lateral Surface Area of Parallelepiped, Side A of Parallelepiped, Side C of Parallelepiped, Angle Beta of Parallelepiped, Angle Gamma 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.

How many ways are there to calculate Surface to Volume Ratio of Parallelepiped?

In this formula, Surface to Volume Ratio of Parallelepiped uses Lateral Surface Area of Parallelepiped, Side A of Parallelepiped, Side C of Parallelepiped, Angle Beta of Parallelepiped, Angle Gamma of Parallelepiped & Angle Alpha of Parallelepiped. We can use 7 other way(s) to calculate the same, which is/are as follows -

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
Surface to Volume Ratio of Parallelepiped = (2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(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)))+(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*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped)*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped)*sin(Angle Alpha of Parallelepiped))))/(Side A of Parallelepiped*Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A 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)))
Surface to Volume Ratio of Parallelepiped = (2*((Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+((Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))))/(Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C 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*(((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped)*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))))/((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C 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)))

Home

FREE PDFs

🔍 Search