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

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

✖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 given Volume, Side B and Side C [LSA]

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

STEP 0: Pre-Calculation Summary

Formula Used

Lateral Surface Area 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 B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))
LSA = 2*((V*sin(∠γ))/(S_c*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2)))+S_b*S_c*sin(∠α))
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

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.
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.
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 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.
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.

STEP 1: Convert Input(s) to Base Unit

Volume of Parallelepiped: 3630 Cubic Meter --> 3630 Cubic 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 Alpha of Parallelepiped: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Angle Beta of Parallelepiped: 60 Degree --> 1.0471975511964 Radian (Check conversion here)
Side B of Parallelepiped: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

LSA = 2*((V*sin(∠γ))/(S_c*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2)))+S_b*S_c*sin(∠α)) --> 2*((3630*sin(1.3089969389955))/(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)))+20*10*sin(0.785398163397301))

Evaluating ... ...

LSA = 1441.95306467929

STEP 3: Convert Result to Output's Unit

1441.95306467929 Square Meter --> No Conversion Required

FINAL ANSWER

1441.95306467929 ≈ 1441.953 Square Meter <-- Lateral Surface Area of Parallelepiped

(Calculation completed in 00.008 seconds)

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

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< Lateral Surface Area of Parallelepiped Calculators

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

LaTeX Go Lateral Surface Area of Parallelepiped = (2*Volume of Parallelepiped*(Side A of Parallelepiped*sin(Angle Gamma of Parallelepiped)+Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))/(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)))

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

LaTeX Go Lateral Surface Area 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 B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))

Lateral Surface Area of Parallelepiped

LaTeX Go Lateral Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))

Lateral Surface Area of Parallelepiped given Total Surface Area

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

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

Lateral Surface Area of Parallelepiped given Volume, Side B and Side C calculator uses Lateral Surface Area 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 B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)) to calculate the Lateral Surface Area of Parallelepiped, The Lateral Surface Area of Parallelepiped given Volume, Side B and Side C formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped, calculated using volume, side B and side C of Parallelepiped. Lateral Surface Area of Parallelepiped is denoted by LSA symbol.

How to calculate Lateral Surface Area of Parallelepiped given Volume, Side B and Side C using this online calculator? To use this online calculator for Lateral Surface Area of Parallelepiped given Volume, Side B and Side C, enter Volume of Parallelepiped (V), Angle Gamma of Parallelepiped (∠γ), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α), Angle Beta of Parallelepiped (∠β) & Side B of Parallelepiped (S_b) and hit the calculate button. Here is how the Lateral Surface Area of Parallelepiped given Volume, Side B and Side C calculation can be explained with given input values -> 1441.953 = 2*((3630*sin(1.3089969389955))/(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)))+20*10*sin(0.785398163397301)).

FAQ

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

The Lateral Surface Area of Parallelepiped given Volume, Side B and Side C formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped, calculated using volume, side B and side C of Parallelepiped and is represented as LSA = 2*((V*sin(∠γ))/(S_c*sqrt(1+(2*cos(∠α)*cos(∠β)*cos(∠γ))-(cos(∠α)^2+cos(∠β)^2+cos(∠γ)^2)))+S_b*S_c*sin(∠α)) or Lateral Surface Area 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 B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)). Volume of Parallelepiped is the total quantity of three-dimensional space enclosed by the surface 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 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 & Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

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

The Lateral Surface Area of Parallelepiped given Volume, Side B and Side C formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped, calculated using volume, side B and side C of Parallelepiped is calculated using Lateral Surface Area 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 B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)). To calculate Lateral Surface Area of Parallelepiped given Volume, Side B and Side C, you need Volume of Parallelepiped (V), Angle Gamma of Parallelepiped (∠γ), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α), Angle Beta of Parallelepiped (∠β) & Side B of Parallelepiped (S_b). With our tool, you need to enter the respective value for Volume of Parallelepiped, Angle Gamma of Parallelepiped, Side C of Parallelepiped, Angle Alpha of Parallelepiped, Angle Beta of Parallelepiped & Side B 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 Lateral Surface Area of Parallelepiped?

In this formula, Lateral Surface Area of Parallelepiped uses Volume of Parallelepiped, Angle Gamma of Parallelepiped, Side C of Parallelepiped, Angle Alpha of Parallelepiped, Angle Beta of Parallelepiped & Side B of Parallelepiped. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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