What is a Parallelepiped?
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.
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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:
S which is the area of the bottom
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
FAQs on Volume of Parallelepiped Formula
Q1. What is the Formula of Rectangular Parallelepiped?
Answer: When the six surfaces of a parallelepiped are rectangular, it is called a rectangular parallelepiped. It's a three-dimensional box framework.
All of the parallel edges here are of the equivalent length.
The rectangular parallelepiped volume formula is:
V= Surface Area × Height.... (1)
In this rectangular parallelepiped formula,
Surface area = the area of a rectangle, i.e.,
Surface area = Length × Width
Therefore, from equation (1),
V = Length × Width × Height
Hence, to calculate the volume, we need to know the measures of the:
Length
Width
Height
Q2. What is the Area of the Parallelepiped Formula?
Answer: Area of parallelepiped A = Length × Height
For the Lateral Surface Area (LSA) of a parallelepiped, the formula is:
LSA = Perimeter of the base × Height
For the Total Surface Area (TSA) of a parallelepiped, the formula is:
TSA = LSA + 2*Base Area
= (Perimeter of the base × Height) + 2*Base Area