02 - Volume of Cube, Cuboid and Cylinder - Class 10 - Maths Video Lecture

in this session we will learn about
volume as you can see that we have three
containers on the first container having
length of 10 centimeter and breadth of
10 centimeter and height is also 10
centimeter such type of container is
called as cube many call it as squared
prism if we pour water into the first
container so first of all it will spread
on the bottom surface and the bottom
surface is square so it will occupy the
area of square that is 10 centimeter
into 10 centimeter if we fill this
container with water at the height of 10
centimeter then the total pore water in
this container will be the area of base
into the height of the container there
is also 10 centimeter and it will give
us 1000 centimeter cube or 1000 cubic
centimeter
now you can see that if we add more
water to this container then it will
spread out of the container that means
the maximum capacity of this container
is thousand cubic centimeter only and
the capacity of any three dimensional
container is called as the volume of
that particular container but water or
any kind of liquid most of the times
measure in terms of liters and 1000
centimeter cube equals 1 liters that
means we can say that we volume off a
cubical container having 10 centimeter
of length is 1000 centimeter cube or 1
liter now let's try to write the general
form of equation for the volume of any
kind of cubical shape so if a cubical
container is having length L centimeter
then the area of base will be squared
and we can write it as L square and
height is also n so we just multiply the
area of base that is L square into the
height L
and it will give us L cubed so the
general form of volume of a cube is L
cube unit cubed let's try to pour water
in the second container which has length
of 10 centimeter depth 15 centimeter and
height 20 centimeter if you look at this
shape then all the dimensions are of
different lengths whereas in the first
case they all were same so if any of the
dimension is different then such kind of
shape is called as cuboid and many call
it as rectangular prism so can you tell
me how much volume of water this
container can have the total pore water
is the area of base that is 10
centimeter into 15 centimeter into the
height of the container that is 20
centimeter and it will give us 3000
centimeter cube so we can say that the
volume of this shape is 3000 centimeter
cubed or 3 liters so let's try to
generalize it
let's take length as L breadth as B and
height as H because all the dimensions
are different so we are using different
alphabets the bottom surface is
rectangular so the area of rectangle is
L into B by multiplying the area of base
into the height that is H we will get
the volume off keyboard so the volume of
cuboid in general terms is L into B into
H unit cubed we can notice one thing
that in such uniform shapes by just
multiplying the area of base into height
we get the volume and now we are having
one more three-dimensional shape a right
circular cylinder if you look at the
base of the right circular cylinder then
the base is circular and the area of any
circle with radius R is PI R squared so
if you multiply the area of circle to
the height then we will get the volume
of a right circular cylinder so first of
all we will
the general expression for the volume of
right circular cylinder and then we will
solve a problem on this
let's take radius R unit and height H
unit so accordingly area of base will be
PI R squared unit squared into h unit
when the volume of cylinder will be PI R
squared H unit cube so let's solve
problem on this suppose a right circular
cylinder having radius R 5 centimeter
and height of 20 centimeter then what
would be the volume of this cylinder so
by applying formula we get one five
seven zero centimeter cubed or we can
say that one point five seven liters so
far we learn about the volume of cube
cuboid and cylinder these were the
standard shapes but some of the times we
can have uneven shapes like this so can
we find out the volume of this this
three-dimensional shape is having length
10 centimeter breadth 8 centimeter and
in this case there are two height one is
4 centimeter and another one is 6
centimeter and we have to find out
volume of this shape how to go about it
first of all we have to break it into
two parts and we will find volume of
each part separately and then add them
up to get the volume of original shape
after separating out at the height of 4
centimeter we got two shapes so let's
start with the bottom part which is a
cuboid with length 10 centimeter breadth
8 centimeter and height 4 centimeter so
it's volume will be 320 centimeter cube
now let's go for the above part if you
notice this shape we can take it as half
of some cuboid with length 10 centimeter
breath L centimeter now remaining height
is 2 centimeter let us find volume of
this keyboard and divide it into half so
that we will get volume of the upper
part
so the volume of cuboid is that is ten
centimeter into eight centimeter into
two centimeter and it will give us one
60 centimeter cubed so therefore half of
this will be 80 centimeter cube which is
the volume of the above part so
therefore the total volume of this shape
will be 320 centimeter cube plus 80
centimeter cube and total we will get
400 centimeter cubed that is 0.4 liters
thank you for watching