Discussion about Cuboid...

1. CUBOID
Presented By:-
Subhajit Manna

2. AIMS & OBJECTIVES
 Students can get a brief concept about Cuboid.
 After the lesson Students can easily evaluate the Area, Volume of
a Cuboid .
 Students can find the length of diagonals of not only a Cuboid
but also a Cube.
 Students can overcome the Real-Life problems including the
objects similar to Cuboid.

3. CONCEPT
FORMING A CUBOID
At first we know how to form a
RECTANGULAR PARALLELOPIPED
Or,
CUBOID.

4. FORMATION
At first we take a
Rectangular piece
ABCD ,shown
In R.H.S.
A D
B C

5. FORMATION
Then we add two
Rectangular pieces D
Similar length of AB
And CD in both sides
AB , CD Of the
rectangle ABCD. B
C
A

6. FORMATION
A
Next, we repeat the same
Process i.e, we add two rectangular D
Pieces Similar length of AD
And CB in both sides
AD , CB Of the
rectangle ABCD.
B
C

7. FORMATION
A
 Then we add a rectangular E
piece EFGH whose length and D H
width are equivalent to the
face ABCD.
B C
F G
Such a figure is Called Rectangular Parallelepiped Or, Cuboid.

8. DEFINITIONS
Rectangular Parallelepiped /Cuboid is a three-dimensional
structure whose all the six faces possess a rectangular shape, in which
the lengths of all the parallel edges are equal and consecutive faces are
perpendicular to each other.
The face, vertex and edges of a
Cuboid are shown in R.H.S.
Bricks are the examples of Cuboid.

9. CUBE
Cube is a special type of Cuboid ,
Whose length ,width and height
of the sides are equal.
The easy example of a Cube in real –life
is a Dice .(Shown in R.H.S.)

10. SURFACE AREA & VOLUME
 Since the Cuboid has Six faces,
So ,
Whole surface area of a Cuboid is
= Sum of the area of 6 faces

11. SURFACE AREA & VOLUME
The area of top and bottom surfaces are
lw , lw
The area of front and back surfaces
are lh , lh
Total area of the two side surfaces
are wh ,wh
Whole Surface area of cuboid = (lw +lw)+ (lh +lh)+ (wh + wh)
= 2(lw + lh + wh) Sqr. Unit
Volume of rectangular prism = lwh Unit3

12. SURFACE AREA & VOLUME
 Since the equal length , height , width of the faces of a cuboid are
called a Cube
So putting , l =w=h in the previous case
We get, The whole surface area of a Cube as
=Sum of the area of 6 equal faces
= 2( l.l + l.l + l.l)=6l2 Sqr Unit
Similarly , the volume of the Cube is
= l . l . l = l3 Unit3
l
l
l

13. DIAGONAL OF A CUBOID
Now , we find the length of a diagonal of a Cuboid.
From the R.H.S. figure ,we see
length=HG= l unit
width=GF= b unit
height=BF= h unit
From the Right-Angled Triangle HGF
the hypotenuse , HF=√(l2 +b2 ) unit
Also , from the Right-Angled Triangle HBF
the hypotenuse , HB=√(l2 +b2+h2 ) unit
Which (HB) is nothing but one of the Diagonals of the
Cuboid ABCDHEFG.
Hence , The length of Diagonal of a Cuboid = √(length2 + width2 +height2)

14. DIAGONAL OF A CUBE
 Since the equal length , height , width of the faces of a cuboid are
called a Cube.
So putting , l = b =h in the previous case
we get one of the Diagonals of a cube as
d =√(l2 + l2+ l2 ) unit
= 3 l unit
Hence , The length of Diagonal of a Cube = 3 x (length of a side)