A box-shaped solid object
that has six identical
square faces.
The concept of a cube was first conceived by the ancient
smurfs, and is recorded in their primitive writings as "Kube"
(sic; this was before the invention of spelling). The figure was
imagined yet not visualized, and mathematicians for
thousands of years could only speculate as to its shape.
Gauss's guess was that its shape resembled a short rolling pin,
flattened in places. The first correct visualization of the cube
was made by the first female mathematician, Renée
Descartes, who applied her Descartesian coordinate system
with the parameters (0, 0, 0, 9am) and (1, 1, 1, noon), where
the first three are spacial coordinates and the last is the Time
Cube index for the implicit earth rotation. This produced a
foundation that, with some rough sketching using a broken
charcoal pencil, created the ideal cube we know today.
What items in every day life have the
shapes of a cylinder, cube, cuboid?
• Cube: sugar cube, child's blocks set, dice
Cuboid: gift box, package of chewing gum,
stick of butter
CUBE:
1. It is square in shape.
2. It is a three dimensional solid figure.
3.Three of its sides meet at each vertex.
4.Formula to find the volume of a cube is a x a x a,when
the edge length is a.
5.Examples of cubes are playing dice.
CUBOID:
1.It is rectangular in shape.
2.It is three dimensional and solid.
3.It is also called a rectangular prism.
4.All its angles are right angles (they measure up to 90
degrees)
5.The opposite faces of a cuboid are equal.
Observe the cuboid and find how many faces it
has? How many corners and how many edges it has?
See the faces are surfaces? Which pair of faces are
equal in size? Do you get any idea to find the surface
area of the cuboid?
• A cube is just a special case of a square prism,
and
• Note: The name "cuboid" comes from "cube"
and -oid (which means "similar to, or
resembling") and so says "it is like a cube".
• Another use of -oid is when we talk about the
Earth being a spheroid (not exactly a sphere,
but close).
A cuboid is a box-shaped object.
It has six flat sides and all angles are
right angles.
And all of its faces are rectangles.
It is also a prism because it has the same
cross-section along a length. In fact it is a
rectangular prism.
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
A cube has 6 equal and plane surfaces. All
the faces of a cube are square in shape.
In a cube there are 6 plane surfaces. There
are 8 vertices and 12 edges.
Parts of a cube:
(i) Face: Face is also known as sides. A cube has six faces and all the
faces of a cube are square in shapes. Each face has four equal sides.
(ii) Edge: When two edges meet each other a line segment formed.
There are 12 edges in a cube. All the 12 edges are equal in length
because all faces are squares. These edges are straight edges.
(iii) Vertex: When three edges meet each other a point formed. There
are 8 vertices in a cube.
(iv) Face Diagonals: Face Diagonals of a cube is the line segment that
joins the opposite vertices of a face. There are 2 diagonals in each face
so altogether there are 12 diagonals in the cube.
(v) Space Diagonals: Space diagonals of a cube are the line segment
that joins the opposite vertices of a cube, cutting through its interior.
There are 4 space diagonals in a cube.
The volume of a cube
is s3 where s is the length of
one edge.
The surface area
of a cube is 6s2, where s is the
length of one edge.
Find the surface area of a cuboid whose
length, breadth and height are 15cm,
12cm and 10cm respectively.
Solution: Length of the cuboid (l) = 15cm
Breadth of the cuboid (b) = 12cm
Height of the cuboid (h) = 10cm
Surface area of a cuboid = 2 (lb + bh + hl)
= 2 (15 12 + 12 10 + 10 15) cm2
= 2 (180 + 120 + 150) cm2
= 2 (450) cm2
= 900 cm2
Find the volume of a block of wood whose
length is 20cm, breadth is 10 cm and
height is 8 cm.
Solution: The block of wood is a cuboid and
the volume of a cuboid = l × b × h
Here, length (l) = 20 cm, breath (b) = 10 cm,
and height (h) = 8 cm
Volume of the block = 20 cm × 10 cm × 8 cm =
1600 cm3
Find the side of a cube whose
surface area is 600 cm2.
Do you know
Capacity:
There is not much difference between the two
words.i.e volume
and capacity
(a)Volume refers to the amount of space
occupied by an object.
(b)Capacity refers to the quantity that a
container holds.
If a water tin holds 100 cm3 of water then the
capacity of the water
tin is 100cm3. Capacity can also measure in
terms of litres.
What we have discussed
1. If l, b, h are the dimensions of cuboid ,
then:
(i) its lateral surface area is 2h (l + b)
(ii) its total surface area is 2 (lb + bh + hl)
2. Lateral Surface area of a cube is 4a²
3. Total Surface area of a cube is 6a²
4. Volume of a cuboid is l × b × h
5. Volume of a cube is side × side × side =
a³
6. 1 cm³ = 1 ml
1 l = 1000 cm³
1 m³ = 1000000 cm³ = 1000 l
= 1 kl(kilolitre)