Surface Area Surface Area and Volume - Maths Class 10

hello friends this video on surface area
and volume part 2 is brought to you by
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before watching this video please make
sure that you have washed part 1 will
take home example the question says a
vessel is in the form of a hollow
hemisphere mounted by a hollow cylinder
the diameter of hemisphere is proteins
in the middle and the total height of a
cell is 13 said we have to find the
inner surface area please note this
inner hair inner surface area although
reference so this is my typical diagram
how if you see this the cushion says a
hollow hemisphere so this is my hollow
hemisphere correct mounted by a hollow
cylinder this is the hollow cylinder so
this is like this this is my cylinder
this you Meissen end up alright this is
my name is the question says the
diameter of hemisphere is putting
sending this is 14 centimeter diameter
is forgive the radius of the seven is 17
correct total height of the vessel is 13
so if this guy is 7 this gay person so
this guy will be 17 13 minus 7 and this
guy is no so see what happened I found
everything wrong see over here
surrender I need radiation height so
radius I know 477 and the height is 6
for a nice plate I need only radius so I
know the radius of the hemisphere now I
can wing it
I can find this up basically I can find
the volume Higgins right let's
understand the cushion sea is height
were 70 from a total height
I knew the height of this hemisphere the
7 so I subtracted this 7 thing because
this guy is 7 and this will be 30 minus
M correct because the whole thing is 30
so I got this elves 680
so the first thing that should come to
our mind is understand the question
properly draw a diagram and then put all
the values find lady is hide everything
so now what I have done I have
everything so four cylinder R is equal
to seven and H is equal to since correct
and for hemisphere R is equal to say
this data mega this is most crucial part
axial so once you have the height of
once you have all the data radius height
of the figures then we start upon the
question say we have to find the inner
surface area of the vessel so as I told
you can break this figure into any spare
and cylinder let me bring this one over
so if I break this this figure becomes
this my cylinder and this is my famous
pool so again break this into two one
correct so I will have to find service
in here surface area of vessel you see
that is nothing but surface area of
hemisphere last surface in your slender
scene either surface in here there is a
common area we subtract so in this case
there is no common area it is no
overlapping in it so we don't need some
time we will see this in the next two
examples so surface area you have to be
two washes so in this case there is no
overlapping area so the proteins are
basically surface area of sphere plus
the place in your cylinder that we can
see because this is a cylinder this is a
spare and for this we can write the
dimensions so 6 this is 7 and this is so
so surface area of any spirit you know
is nothing but pi RH this is the formula
we have learned in the phosphors surface
area of hemisphere is by rh surface area
of
where is 4pi sorry surface area of
hemisphere is 2 PI R square by r so
surface area of hemisphere is 2 pi r
square surface area of sphere is 4
players plus surface area of cylinder
surface area of cylinder is PI R H see
easy to remember also PI R is the
circumference of the circle
you take the circle you extend the
height become 2 pi RH so this is the
surface area of the Snyder correct
because 2 pi R is the circumference of
the circle here and in this certainly
extend the height you get 2 pi R into H
2 pi RH becomes surface area of a
cylinder and 2 PI R square is surface
area in sphere they'll just put the
values here so this becomes 2 by 7 you
are is 7 into 7 plus 2 into 22 by 7 into
re 7 and H is so correct this gets
cancelled so what we get here 44 camera
here 44 into 7 plus 6 that there's 44
into 13 and if you solve this further
you get 570 now we talk about surface
area and we are talking about
centimeters so we'll say st. evader why
this way please don't forget aggregation
that you need that is critical here
since we are talking about hemisphere
surface area surface area so in
centimeter square very simple what you
have done here you give the figure we
have broken this figure into Hemisphere
and cylinder form those a case in your
hemisphere some form the helio of
cylinder and then
let's take one more example a tie is in
the form of the cone shape of radius
three point five centimeter mountain on
a hemisphere of same radius the total
height of the toys fifteen point five we
have to find total surface area similar
to the same pushing in zero cylinder it
is a coal hand so this is the toy we're
talking about and in this toy if we see
the radius is this guy is three point
five individual so this guy is also
three point percentage correct total
height is fifteen point five so this guy
will become 2l pipe because total high
is 50 15.5 from that we subtract three
point five you get to it
correct see this guy is fifteen point
five this guy is three this guy has to
be channels three point five minus 12
the ester so what we should know for
foam we should know our our we know is
three point five H X is 2
so we know everything about point or can
be spare we should know our and RS 3
point so we know all the values first
part is done correct we do you the
diagram broccoli and we know the units
in the values out radius right now we
have to find total surface area of the
time so again same thing service area of
toy will be equal to surface area of
home plus surface area hemisphere but
you see this also this is credit using
to power draw this again this is my home
and this is my home this way if you
break this figure this is exactly what
we are talking about and this is 12
right
and this radius we know is three point
so we have broken this cone into this
2pi in their basic part because you know
the volume is a piece of your phone into
the volume and surface area are spared
so we can find them but it was difficult
for us to find the rope envelope of this
figure now surface in your cone is PI R
L where L is the latent right pillows
and surface area of hemisphere is 2 PI R
star L is something which we bone 1 so
let us find the value of L is the latent
height we go this is the ligand right if
you see in this triangle will remind the
elephant as you see this triangle in
this triangle here
this is L this a behind this is this is
height that is 12 and this is right here
that is 3.5 and this is a right angle
you can see this this is how it is so L
is nothing but root of X square plus R
square because in this triangle also if
you see this is L this is H and this is
r so you get this a right triangle so L
is nothing but root of s square plus R
square music Pythagoras now you put the
values here so this becomes root or 2 L
square plus 3 point 5 is 7 by T Square
so expand this further we where 144 plus
49 right Oh what are you get Oh common
before 144 into voice play 76 last for
me this becomes a loop of 625
or and this becomes Mindy microwave so L
is 25 items so I'll put the value 0 pi
is 22 by 7 RS M by L is 25 but true in
the pie is 27 I'll 7 baby correct so if
you solve this this becomes 1 37 point 5
and this becomes 7 itself is Nancy this
is pencil and the sketch 27 and this
becomes 1 37 point 5 this cancel those
becomes 11 so when if I will evidence
this way so we saw this this moves to
one point now since we are talking about
surface area and this is in centimeter
so this will be centimeter Square and
that is so I found total area of the toy
to be 2 1 4 point 5 centimeter and how I
form surface area surface area
I found surface area of the common I
found such a server of the hemisphere
and then added this to get surface area
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