01 - Surface Area of Cube, Cuboid & Cylinder - Class 10 - Maths Video Lecture

hello everyone we are going to study
about surface area and volume but in
this session we are only going to
discuss about surface area before going
into details let us see what is surface
now suppose we have a cupboard and we
want to paint this cupboard from outside
so total portion of this cupboard which
we can paint from outside is surface of
this cupboard in the example of this
cupboard we can see that we have painted
this cupboard from six sides front and
back top of this cupboard and bottom
left side and right side here we can see
that there are total 6 faces which we
have painted from outside and all these
faces of the scoreboard is called
surface of this cupboard so what do we
call a surface the uppermost or exposed
portion of any object and what do we
call the surface area the area occupied
by that surface first we are actually
surrounded by these objects only like
bucket TV gas cylinder so in this
session we will discuss how to find out
total surface area of some important
objects let us start with the cube first
of all we will see pore shape do we call
a cube as we all know the area of a
square with side L is L square now
suppose I want to make a box using such
square shapes who is having area of L
square this is our base which is having
four sides and we are going to create
wall on these four sides as you have
already created a wall so let us draw
the next one this is my second wall this
would be third wall and the front would
be the fourth wall and the top surface
would be the last surface of this box so
in this shape of a cube we can see that
there are total six surfaces and all the
surface is having same area l square top
and bottom and four walls we have seen
that we have used six surfaces of having
same area L square so total area would
be L square plus L square six times and
we would get six l square so six L
square would be the total surface area
of this cube having length as L where L
can be any
so shape of a cube is this and we have
got the formula for total surface area
of a cube so let us consider a real-life
example in dice we can see their total
six surfaces all the surfaces are having
same area and all the surfaces are in
the shape of a square let us solve a
problem based on this formula suppose we
are asked to find out the total surface
area of a cube having length as five
centimeter so by using the formula for
surface area 6l square we would get 150
centimeter square so we have got the
total surface area of a cube having
length as 5 centimeter our second shape
for this session is a cuboid first of
all we will see what is the difference
between cube and cuboid cube is a shape
having six surfaces all the surfaces of
a cube are square shaped while in cuboid
all the surfaces are rectangular and
only opposing surfaces are equal to each
other
suppose length of this cuboid as L
breadth as B and height as H let us find
surface area of top surface we can see
our top surface looks something like
this we can see that this shape is
rectangular having two sides L & P and
as we all know the area of a rectangle
with sides L and B is L into B since I
am having two surfaces top surface and
bottom surface so I would add 1 lb more
now we will find out surface area of
front surface this surface is something
like this having length L and breadth as
H so area of this rectangle would be L
into H since I am having two such
surfaces front surface and back surface
so I would add 1 LH more to get the area
of 2 such surfaces let us find the area
of left surface we can see that left the
surface is this which is having side B
and H so what would be the area of this
rectangle B into H right and since I am
having two surfaces left surface and the
right surface so I would add
BH here we can see that we have got the
total surface area of this cuboid we
have found out the surface area of top
surface and bottom surface as lb plus lb
area of front surface and back surface
as LH + LH an area of left surface and
right surface as BH plus BH so our
formula become lb + lb - lb LH + LH - LH
and BH + bh 2 bh if we take 2 as a
common factor we can also write it as 2
into bracket lb + bh + LH this is the
total surface area of a cuboid having
length L D and edge where L B and H can
be any number an eraser is the best
example of a cuboid let us solve a
problem based on this formula suppose I
am having an eraser having length L as 2
centimeter breadth as 3 centimeters and
height as 4 centimeter then what will be
the total surface area of this eraser 52
centimeters square so we have got the
total surface area of an eraser having
length 2 centimeter depth 3 centimeter
and height 4 centimeter our third and
last shape of this session is a right
circular cylinder right circular
cylinder looks something like this
suppose this cylinder is having height H
and radius R in right circular cylinder
top and bottom surface are in the shape
of a circle if we take out top and
bottom surface of this cylinder
you'd get two circles and our original
cylinder would become a pipe which is
open from top and bottom so radius of
these two circles would be R and if we
cut our cylinder to open it up we would
get a shape of a rectangle and as we all
know the circumference of a circle with
radius R is 2 PI R so we would get the
length of this rectangle as 2 PI R since
this length is the circumference of this
circle and
would be the height of the cylinder edge
so finally we got a rectangle where is
having length two PI R and depth H so we
would find out the surface area of this
rectangle and surface area of these two
circles surface area of this rectangle
would be two pi RH multiplication of
these two sides and as we all know the
area of a circle with radius R is PI R
square and I am having two such circles
so I can write PI R square plus PI a
square so our formula for totals of this
area of a cylinder would be 2 PI R
square plus 2 pi RH and if we take 2 PI
R as a common factor we would get 2 pi R
into bracket r plus h where R and H can
be any numbers according tin is a best
example of a cylinder let us solve a
problem based on this formula let us
find out the total surface area of this
tin having radius R is 4 centimeter and
height 10 centimeter so the dualist
surface area of this tin would be 112 5
centimeter square let's have a recap of
this session first of all we studied
what is surface then wasted it what is
surface area then we defined three
shapes cube cuboid and cylinder and we
found out the total surface area of
these three shapes respectively and we
solve three problems based on these
formulas thank you