Volume of Parallelepiped Calculator

✖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%
✖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 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%
✖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%

✖Volume of Parallelepiped is the total quantity of three-dimensional space enclosed by the surface of the Parallelepiped.ⓘ Volume of Parallelepiped [V]

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Formula

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Volume of Parallelepiped

Formula

`"V" = "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

`"3630.002m³"="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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Volume of Parallelepiped Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
V = 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 2 Functions, 7 Variables

Functions Used

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

Volume of Parallelepiped - (Measured in Cubic Meter) - Volume of Parallelepiped is the total quantity of three-dimensional space enclosed by the surface 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.
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 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.
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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = S_a*S_b*S_c*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2)) --> 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 ... ...

V = 3630.00200223542

STEP 3: Convert Result to Output's Unit

3630.00200223542 Cubic Meter --> No Conversion Required

FINAL ANSWER

3630.00200223542 ≈ 3630.002 Cubic Meter <-- Volume of Parallelepiped

(Calculation completed in 00.020 seconds)

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< 11 Volume of Parallelepiped Calculators

Volume of Parallelepiped given Totall Surface Area, Side A and Side B

Go Volume of Parallelepiped = Side A of Parallelepiped*Side B of Parallelepiped*(Total Surface Area of Parallelepiped/2-Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))/(Side A of Parallelepiped*sin(Angle Beta of Parallelepiped)+Side B 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))

Volume of Parallelepiped given Total Surface Area, Side B and Side C

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

Go Volume of Parallelepiped = Side A of Parallelepiped*Side C of Parallelepiped*(Total Surface Area of Parallelepiped/2-Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))/(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))

Volume of Parallelepiped given Lateral Surface Area, Side A and Side C

Go Volume 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))

Volume of Parallelepiped given Lateral Surface Area, Side B and Side C

Go Volume of Parallelepiped = Side C of Parallelepiped/sin(Angle Gamma of Parallelepiped)*(Lateral Surface Area of Parallelepiped/2-Side B 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))

Volume of Parallelepiped given Lateral Surface Area, Side A and Side B

Go Volume of Parallelepiped = Side A of Parallelepiped/sin(Angle Alpha of Parallelepiped)*(Lateral Surface Area of Parallelepiped/2-Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma 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 given Total Surface Area and Lateral Surface Area

Go 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))

Volume of Parallelepiped given Perimeter, Side A and Side C

Go Volume of Parallelepiped = Side A of Parallelepiped*Side C of Parallelepiped*(Perimeter of Parallelepiped/4-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))

Volume of Parallelepiped given Perimeter, Side B and Side C

Go Volume of Parallelepiped = Side B of Parallelepiped*Side C of Parallelepiped*(Perimeter of Parallelepiped/4-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))

Volume of Parallelepiped given Perimeter, Side A and Side B

Go Volume 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))

Volume of Parallelepiped

Go 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))

< 2 Volume of Parallelepiped Calculators

Volume of Parallelepiped given Total Surface Area and Lateral Surface Area

Volume of Parallelepiped

Volume of Parallelepiped 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 Volume of Parallelepiped?

Volume of Parallelepiped calculator uses 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)) to calculate the Volume of Parallelepiped, The Volume of Parallelepiped formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped. Volume of Parallelepiped is denoted by V symbol.

How to calculate Volume of Parallelepiped using this online calculator? To use this online calculator for Volume of Parallelepiped, enter Side A of Parallelepiped (S_a), Side B of Parallelepiped (S_b), 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. Here is how the Volume of Parallelepiped calculation can be explained with given input values -> 3630.002 = 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 Volume of Parallelepiped?

The Volume of Parallelepiped formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped and is represented as V = 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 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)). 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, Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex 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, 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.

How to calculate Volume of Parallelepiped?

The Volume of Parallelepiped formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped is calculated using 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)). To calculate Volume of Parallelepiped, you need Side A of Parallelepiped (S_a), Side B of Parallelepiped (S_b), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α), Angle Beta of Parallelepiped (∠β) & Angle Gamma of Parallelepiped (∠γ). With our tool, you need to enter the respective value for Side A of Parallelepiped, Side B of Parallelepiped, Side C of Parallelepiped, Angle Alpha of Parallelepiped, Angle Beta of Parallelepiped & Angle Gamma 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 Volume of Parallelepiped?

In this formula, Volume of Parallelepiped uses Side A of Parallelepiped, Side B of Parallelepiped, Side C of Parallelepiped, Angle Alpha of Parallelepiped, Angle Beta of Parallelepiped & Angle Gamma of Parallelepiped. We can use 11 other way(s) to calculate the same, which is/are as follows -

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

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