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

✖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 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%
✖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 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 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%

✖Volume of Parallelepiped is the total quantity of three-dimensional space enclosed by the surface of the Parallelepiped.ⓘ Volume of Parallelepiped given Lateral Surface Area, Side B and Side C [V]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
V = S_c/sin(∠γ)*(LSA/2-S_b*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

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 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 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.
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 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 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.

STEP 1: Convert Input(s) to Base Unit

Side C of Parallelepiped: 10 Meter --> 10 Meter No Conversion Required
Angle Gamma of Parallelepiped: 75 Degree --> 1.3089969389955 Radian (Check conversion here)
Lateral Surface Area of Parallelepiped: 1440 Square Meter --> 1440 Square Meter No Conversion Required
Side B of Parallelepiped: 20 Meter --> 20 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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = S_c/sin(∠γ)*(LSA/2-S_b*S_c*sin(∠α))*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2)) --> 10/sin(1.3089969389955)*(1440/2-20*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 ... ...

V = 3623.88356356897

STEP 3: Convert Result to Output's Unit

3623.88356356897 Cubic Meter --> No Conversion Required

FINAL ANSWER

3623.88356356897 ≈ 3623.884 Cubic Meter <-- Volume of Parallelepiped

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Parallelepiped » Volume of Parallelepiped » Volume of Parallelepiped given Lateral Surface Area, Side B and Side C

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< Volume of Parallelepiped Calculators

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

LaTeX 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

LaTeX 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 Total Surface Area and Lateral Surface Area

LaTeX 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

LaTeX 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))

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

LaTeX Go

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 given Lateral Surface Area, Side B and Side C?

Volume of Parallelepiped given Lateral Surface Area, Side B and Side C calculator uses 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)) to calculate the Volume of Parallelepiped, The Volume of Parallelepiped given Lateral Surface Area, Side B and Side C formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped, calculated using lateral surface area, side B and side C of Parallelepiped. Volume of Parallelepiped is denoted by V symbol.

How to calculate Volume of Parallelepiped given Lateral Surface Area, Side B and Side C using this online calculator? To use this online calculator for Volume of Parallelepiped given Lateral Surface Area, Side B and Side C, enter Side C of Parallelepiped (S_c), Angle Gamma of Parallelepiped (∠γ), Lateral Surface Area of Parallelepiped (LSA), Side B of Parallelepiped (S_b), Angle Alpha of Parallelepiped (∠α) & Angle Beta of Parallelepiped (∠β) and hit the calculate button. Here is how the Volume of Parallelepiped given Lateral Surface Area, Side B and Side C calculation can be explained with given input values -> 3623.884 = 10/sin(1.3089969389955)*(1440/2-20*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 Volume of Parallelepiped given Lateral Surface Area, Side B and Side C?

The Volume of Parallelepiped given Lateral Surface Area, Side B and Side C formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped, calculated using lateral surface area, side B and side C of Parallelepiped and is represented as V = S_c/sin(∠γ)*(LSA/2-S_b*S_c*sin(∠α))*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2)) or 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)). Side C 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, 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 B 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.

How to calculate Volume of Parallelepiped given Lateral Surface Area, Side B and Side C?

The Volume of Parallelepiped given Lateral Surface Area, Side B and Side C formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Parallelepiped, calculated using lateral surface area, side B and side C of Parallelepiped is calculated using 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)). To calculate Volume of Parallelepiped given Lateral Surface Area, Side B and Side C, you need Side C of Parallelepiped (S_c), Angle Gamma of Parallelepiped (∠γ), Lateral Surface Area of Parallelepiped (LSA), Side B of Parallelepiped (S_b), Angle Alpha of Parallelepiped (∠α) & Angle Beta of Parallelepiped (∠β). With our tool, you need to enter the respective value for Side C of Parallelepiped, Angle Gamma of Parallelepiped, Lateral Surface Area of Parallelepiped, Side B of Parallelepiped, Angle Alpha of Parallelepiped & Angle Beta 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 C of Parallelepiped, Angle Gamma of Parallelepiped, Lateral Surface Area of Parallelepiped, Side B of Parallelepiped, Angle Alpha of Parallelepiped & Angle Beta of Parallelepiped. We can use 3 other way(s) to calculate the same, which is/are as follows -

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))
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))

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