Class 10 Exam > Class 10 Videos > Major Minor Sector Segements - Areas Related to Circles
Major Minor Sector Segements - Areas Related to Circles Video Lecture - Class 10
FAQs on Major Minor Sector Segements - Areas Related to Circles Video Lecture - Class 10
| 1. What are major and minor sectors in the context of circle sectors? |  |
Ans. Major and minor sectors are segments formed within a circle by two radii and an arc. The major sector is the larger part of the circle enclosed by the arc and two radii, while the minor sector is the smaller part of the circle enclosed by the arc and two radii.
| 2. How are major and minor sectors related to the area of a circle? | |
Ans. The area of a major sector is calculated by finding the fraction of the total area of the circle that the central angle of the sector represents and multiplying it by the total area of the circle. Similarly, the area of a minor sector is calculated in the same way but with the central angle of the minor sector.
| 3. Can the area of a major sector be greater than the area of the circle? | |
Ans. No, the area of a major sector cannot be greater than the area of the circle. The area of the major sector is always a fraction of the total area of the circle, which means it will always be smaller than or equal to the area of the circle.
| 4. How can we find the area of a minor sector if we know the central angle and the radius of the circle? | |
Ans. To find the area of a minor sector, we can use the formula: Area = (θ/360) x πr², where θ is the central angle in degrees and r is the radius of the circle. By substituting the values of θ and r into the formula, we can calculate the area of the minor sector.
| 5. Are major and minor sectors used in real-world applications? | |
Ans. Yes, major and minor sectors are used in various real-world applications. For example, they are used in the calculation of the area of a sector in fields such as engineering, architecture, and physics. Understanding major and minor sectors is also important in geometry and trigonometry, which are fundamental subjects in mathematics.
Text Transcript from Video
hello friends this video on areas
related to circles part 5 is brought you
by exam viacom no more fear from exam
before watching this video please make
sure that you have washed part 1 - part
4 let's say understand the sector of the
circle so they are too kind of sector
one is major sector and one else - if
you have a circle the center draw two
lines and this point that says the
circle the minor one is called minor are
the major is gone nature of example we
have a motion like this draw this point
so this is called minor and this makes
good major of what this angle is less
than 180 so the area which is smaller
where the angle is the third one it is
called minor sector this holding is
called sector and this thing is called
of a sector so this is nothing but major
sector and this guy is nothing one minor
sector right similarly this line from A
to B Scott Park is called minor arc and
from here a example a say a Q this line
from here there this called major rock
and this one a PV is called minor a PV
is called minor now let's see what is
major and minor segments if you have the
circle big circle and this chord AV
divide the circle into two parts the one
which covers maximum area or more areas
called major segment and the one which
covers lesser area is called Maya
segments the one the blue is minor
and the one in the widest reach example
I mean we haven't circle yes and this is
a car EB which cuts the white circle in
area one into the one in the lesser area
is called minor segment and the one with
the big area is called major sing so
please note a difference in case of
segment this is a chord that divides
circle into area in case of are you have
three years that divide the circle into
two alien example this is minor sector
and this is major sector so this is the
example of sector where the area is
divided by the radius at the center and
in this case it is the cord that divides
so it is segment please note in case of
segment the core divides circle into two
parts in case of sector it is this
radius and this center it is arc this
divides occur into two bars so this is
the major sector
this is minor sector similarly here this
is major segment and this is -8 so let's
have some node for sector and segment so
I we write segment or sector in normal
case without minor major we need - a and
- sector that means when I say sector a
sector some sector of circle that means
we are talking about minor sector and I
am saying some segment of mini circle I
am saying I'm talking about minor
segment
so if main a minor major is not
specified the default one is minor only
correct if I just a segment just a
sector I mean minor sector and minor
segment so let's see the area of sector
of a circle so in this case if you have
this circle and we have a sector and the
angles of industry down the radius is
our area of the sector the blue part
will be theta by three-sixty
two PI R square logically also if you
see you start from a one point the whole
circle is 360 really right it's out of
this series I am talking about a ring
Cheeta for the area so the area will be
theta by three-sixty if you put theta is
equal to 180 you put it as equal to 180
you get 180 by 360 by PI R squared is PI
by 2 R squared it is area of this signal
correct so the area of sector the
default formula is theta by three-sixty
into PI R square where theta is the
angle subtended by the radius and C 60
we know is the polar angle will be
constant and PI R square where R is
radius of the circle
similarly the length of the sector for
example this length of sector this
sector if you want to find this length a
PV this will be theta by three-sixty
into two PI R so you see Rho PI R square
it is 2 PI R when we are talking about
the area of the sector we are telling PI
R square when I am talking about the
length of the sector I am doing 2 PI R Y
because this theta is my intercept and
net this is you the total angle theta
wise exist you be the angle subtended by
the length when this thing so that will
be a TD correct this will be theta by
three-sixty into two PI R this is
nothing but if this length is the length
we are talking about theta by
three-sixty into two PI R similarly the
area of the segment so we have this card
AV this divides the circle into two half
or not exactly half two part part one
and this whole thing is part two so we
have to find the area of the segment in
the area of the blue coloration so for
this there is no direct formula so what
we have to do we have to first find the
area of the sector the whole sector and
then you subtract this triangle a movie
it is we define the area of sector
o a PV this for
they need to find this we can find
there's nothing but theta by three-sixty
into PI R square from this you have to
subtract this triangle ooh a V and then
we'll get the idea you'll see there is
no direct formula to find the area of
the segment to find the area segment you
do find see how it is constructed so in
this case it is area of the whole sector
- area of the triangle
we'll take some examples you define the
area of the sector of the circle with
radius 6 centimeter and angle subtended
by sector is 60 degrees this angle is 60
degree and this R is 6 entry so we have
to find here any of the sector right so
area of sector we know the formula is
what ETA by 360 degree since it is area
of sector so it is PI R square all right
we put the value theta is equal to 16
and by 360 degree is constant PI they
say 20 by 7 R is 6
does it correct so this becomes 1 by 6 +
6 6 cancels so what I get is 113 by 7
and the unit is centimeter so it will be
a centimeter square why because we're
talking about area and that is miles
where is it 1 to find the area of sector
theta is given theta by three-sixty into
PI R square here are also given find the
gun
let's take home example find the idea of
the quadrant of a circle circumferences
when we keep sending it need to find the
area of this quadrant disagree of this
water where the circumference is
solution so we know that area of the
quadrant is nothing but the angles of it
is 9 degree that is 90 degree by 360
degree into PI R square so we know theta
and D we know we have to find our love
ah how to find the value of r we had
told circumference Trinity since the
governor is going to do we can find the
value of R how
you know that circumference is nothing
but 2 PI R and this value is nothing but
when you do something but going to PI a
stratum 2 by 7 do I so from this if you
so all we get R is going to this cancels
7 by 2 so R is 7 by 2 we have got the
mango path now where to find the area of
coordinate area of quadrant please don't
do the quadrant quadrant means this area
because one complete circle we divide
into 4 part coordinates for fourth part
this might be V and this fertility of it
on this part is nothing but 90 degree by
360 degree but 3 times 19 2 by PI is way
to verse 7 R square it is 7 by 2 in
descent way to correct but the formula
we are using is theta by three-sixty PI
R square this becomes on my phone and
solve this bush and this gets cancelled
11 this was the cancel so what you get
you get 7 to 11 77 when you do is 1877
by 8 this is centimetre we are talking
about area so the unit is centimeter
square in this man's very simple what we
have done we first found the radius and
then we use formula aerial column is
nothing but theta by three-sixty PI R
square theta is 90 and RS the radius
which we form God rest thank you visit
exam viacom to watch free education
videos try free online tests get the
best quality study materials study from
the best tutors and mentors and much
more thanks and serene
related to circles part 5 is brought you
by exam viacom no more fear from exam
before watching this video please make
sure that you have washed part 1 - part
4 let's say understand the sector of the
circle so they are too kind of sector
one is major sector and one else - if
you have a circle the center draw two
lines and this point that says the
circle the minor one is called minor are
the major is gone nature of example we
have a motion like this draw this point
so this is called minor and this makes
good major of what this angle is less
than 180 so the area which is smaller
where the angle is the third one it is
called minor sector this holding is
called sector and this thing is called
of a sector so this is nothing but major
sector and this guy is nothing one minor
sector right similarly this line from A
to B Scott Park is called minor arc and
from here a example a say a Q this line
from here there this called major rock
and this one a PV is called minor a PV
is called minor now let's see what is
major and minor segments if you have the
circle big circle and this chord AV
divide the circle into two parts the one
which covers maximum area or more areas
called major segment and the one which
covers lesser area is called Maya
segments the one the blue is minor
and the one in the widest reach example
I mean we haven't circle yes and this is
a car EB which cuts the white circle in
area one into the one in the lesser area
is called minor segment and the one with
the big area is called major sing so
please note a difference in case of
segment this is a chord that divides
circle into area in case of are you have
three years that divide the circle into
two alien example this is minor sector
and this is major sector so this is the
example of sector where the area is
divided by the radius at the center and
in this case it is the cord that divides
so it is segment please note in case of
segment the core divides circle into two
parts in case of sector it is this
radius and this center it is arc this
divides occur into two bars so this is
the major sector
this is minor sector similarly here this
is major segment and this is -8 so let's
have some node for sector and segment so
I we write segment or sector in normal
case without minor major we need - a and
- sector that means when I say sector a
sector some sector of circle that means
we are talking about minor sector and I
am saying some segment of mini circle I
am saying I'm talking about minor
segment
so if main a minor major is not
specified the default one is minor only
correct if I just a segment just a
sector I mean minor sector and minor
segment so let's see the area of sector
of a circle so in this case if you have
this circle and we have a sector and the
angles of industry down the radius is
our area of the sector the blue part
will be theta by three-sixty
two PI R square logically also if you
see you start from a one point the whole
circle is 360 really right it's out of
this series I am talking about a ring
Cheeta for the area so the area will be
theta by three-sixty if you put theta is
equal to 180 you put it as equal to 180
you get 180 by 360 by PI R squared is PI
by 2 R squared it is area of this signal
correct so the area of sector the
default formula is theta by three-sixty
into PI R square where theta is the
angle subtended by the radius and C 60
we know is the polar angle will be
constant and PI R square where R is
radius of the circle
similarly the length of the sector for
example this length of sector this
sector if you want to find this length a
PV this will be theta by three-sixty
into two PI R so you see Rho PI R square
it is 2 PI R when we are talking about
the area of the sector we are telling PI
R square when I am talking about the
length of the sector I am doing 2 PI R Y
because this theta is my intercept and
net this is you the total angle theta
wise exist you be the angle subtended by
the length when this thing so that will
be a TD correct this will be theta by
three-sixty into two PI R this is
nothing but if this length is the length
we are talking about theta by
three-sixty into two PI R similarly the
area of the segment so we have this card
AV this divides the circle into two half
or not exactly half two part part one
and this whole thing is part two so we
have to find the area of the segment in
the area of the blue coloration so for
this there is no direct formula so what
we have to do we have to first find the
area of the sector the whole sector and
then you subtract this triangle a movie
it is we define the area of sector
o a PV this for
they need to find this we can find
there's nothing but theta by three-sixty
into PI R square from this you have to
subtract this triangle ooh a V and then
we'll get the idea you'll see there is
no direct formula to find the area of
the segment to find the area segment you
do find see how it is constructed so in
this case it is area of the whole sector
- area of the triangle
we'll take some examples you define the
area of the sector of the circle with
radius 6 centimeter and angle subtended
by sector is 60 degrees this angle is 60
degree and this R is 6 entry so we have
to find here any of the sector right so
area of sector we know the formula is
what ETA by 360 degree since it is area
of sector so it is PI R square all right
we put the value theta is equal to 16
and by 360 degree is constant PI they
say 20 by 7 R is 6
does it correct so this becomes 1 by 6 +
6 6 cancels so what I get is 113 by 7
and the unit is centimeter so it will be
a centimeter square why because we're
talking about area and that is miles
where is it 1 to find the area of sector
theta is given theta by three-sixty into
PI R square here are also given find the
gun
let's take home example find the idea of
the quadrant of a circle circumferences
when we keep sending it need to find the
area of this quadrant disagree of this
water where the circumference is
solution so we know that area of the
quadrant is nothing but the angles of it
is 9 degree that is 90 degree by 360
degree into PI R square so we know theta
and D we know we have to find our love
ah how to find the value of r we had
told circumference Trinity since the
governor is going to do we can find the
value of R how
you know that circumference is nothing
but 2 PI R and this value is nothing but
when you do something but going to PI a
stratum 2 by 7 do I so from this if you
so all we get R is going to this cancels
7 by 2 so R is 7 by 2 we have got the
mango path now where to find the area of
coordinate area of quadrant please don't
do the quadrant quadrant means this area
because one complete circle we divide
into 4 part coordinates for fourth part
this might be V and this fertility of it
on this part is nothing but 90 degree by
360 degree but 3 times 19 2 by PI is way
to verse 7 R square it is 7 by 2 in
descent way to correct but the formula
we are using is theta by three-sixty PI
R square this becomes on my phone and
solve this bush and this gets cancelled
11 this was the cancel so what you get
you get 7 to 11 77 when you do is 1877
by 8 this is centimetre we are talking
about area so the unit is centimeter
square in this man's very simple what we
have done we first found the radius and
then we use formula aerial column is
nothing but theta by three-sixty PI R
square theta is 90 and RS the radius
which we form God rest thank you visit
exam viacom to watch free education
videos try free online tests get the
best quality study materials study from
the best tutors and mentors and much
more thanks and serene
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Nov 23, 2024 Last updated |
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