[Maths Class Notes] on Volume of Parallelepiped Formula Pdf for Exam

To work with any parallelepiped formula, we need to know what precisely a parallelepiped is. A parallelepiped is a three-dimensional structure constructed by six parallelograms in symmetry. A parallelepiped is identified as three sets of four parallel edges with equally sized edges within each set.

Geometric Figures Associated With Parallelepiped

The prism’s base planes may very well be considered as any of the three pairs of parallel sides.

A cuboid is correlated to a rectangle in much the same fashion as a cube is closely similar to a square, and similarly, a parallelepiped is related to a parallelogram.

What Do You Need to Know to Find the Volume of a Parallelepiped?

To find the parallelepiped formula for the volume, we need to know the measures of two things:

1. S which is the area of the bottom

2. H which is the height of the parallelepiped

What is the Formula of Volume of a Parallelepiped?

The formula is:

V=S×h

Where,

V = the volume of the parallelepiped

Also, the formula for volume of parallelepiped = absolute value of the scalar triple product, i.e., a · (b × c)

What Is The Volume Of A Parallelepiped Formula In A Vector?

The volume of the parallelepiped spanned by a, b, and c is

Volume V=area of base⋅height=∥a×b∥ ∥c∥ |cosϕ|

             =|(a×b)⋅c|.

Since the angle between c and a×b in the formula of volume of parallelepiped might potentially be greater than π/2 based on the order between a and b, we will have to use the absolute value in the volume of the parallelepiped formula vector.

Solved Example for Rectangular Parallelepiped Formula

Example1:

The size of the parallelepiped is 9 ft. long, 6 ft. wide, and 12 ft. deep. Calculate the volume.

Solution:

According to the formula of rectangular parallelepiped,

Volume V= Length × Width × Height (From equation (1) volume of parallelepiped formula)

Therefore, V= 9*12*6 =648ft³

Example2:

Find the volume of parallelepiped where 40cm2 is the area of the bottom, and 30 cm is the height of the parallelepiped.

Solution:

According to the volume of parallelepiped formula,

V=S*H

where S=40 cm2

H= 30cm

Therefore, V=40*30=120 cm³