Examples: Circumference and Area of Circle (Part- 3) Video Lecture - Class 7

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question number 6 a circular flowerbed
is surrounded by a part four meters wide
so you have a circular flowerbed like
this and then this flower bed is
surrounded by a path all around it like
this so the circle is not drawn very
neatly so but in the question it is
given that the width of this path is
four sent four meters every mail so
wherever you measured this width this
width is 4 meters the diameter of the
flowerbed is 66 meters that means this
entire diameter is 66 meters let's
assume this is the center what is the
area of the part so we have to find out
the area of this path so the area of
this particular path how do we find this
out so we will again find out the area
of the bigger circle and then we will
subtract the area of the smaller circle
from the bigger circle so that is how we
do it so let us first try to find out
the area of the bigger circle so the
area of the bigger circle would be PI R
square now what is the area like what
what would be the radius for the bigger
circle so 66 meter is diameter for the
smaller circle so when you consider the
bigger circle that what would be the
diameter the diameter would be 66 plus 4
on this side plus 4 on this side right
so the diameter of the bigger circle is
66 plus 4 plus 4 so like a sine theta so
diameter of bigger
circle is equal to 66 plus 4 plus 4
which is equal to 74 meters and what is
the diameter of the smaller circle
diameter of the smaller circle is 66
meters now if we know diameter of both
the circle we can find out the radius
also because area of the bigger circle
is PI R square and radius is half of
diameter that is 74 by 2 whole square so
this is equal to PI into 37 into 37 so
37 into 37 is 1 3 6 9 pi so this is the
area of the bigger circle so in a
similar way let us find out the area of
the smaller circle so for the smaller
circle radius is equal u will be equal
to 1/2 of a meter and the diameter is 66
so the radius would be 66 divided by 2
whole square so this is PI into 33 into
33 this is equal to 1 0 8 9 pi so let us
denote the area of the smaller circle as
a 2 and let us denote the area of the
bigger circle as a 1 therefore what
would be the area of the park so area of
part would be area of the bigger circle
minus area of the smaller circle so that
is equal to 1 3 6 9 pi minus 1 0 8 9 5
so this is equal to 285 that is equal to
so when you put the value of pi is 3.14
orders to AP into 3.14 that is equal to
8
seventy nine point two centimeter square
sorry this would be meter square because
everything is given in meters so eight
seventy nine point two meter square so
you see this is the approach that you
should follow to solve real-life
problems based on area and circumference
of circles so the firsts your first step
should always be to draw a rough diagram
so that you get a clear understanding of
the problem question number seven Shazi
took a wire of length forty four
centimeters and bent it into the shape
of a circle so let's say this is the
wire that Charles Lee had and she bent
it in the shape of a circle like this
and the questions he is that the total
length of this wire is 44 centimeters so
the length of the wire is nothing but
the circumference of the circle so
circumference of the circle is 2 PI R so
2 PI R is given as 44 centimeters right
because the length of the wire forms the
total length of the boundary of the
circle which is nothing but the
circumference now we have to find out
the radius of the circle that's pretty
simple 2 PI R is equal to 44 therefore R
is equal to 44 divided by 2 pi so we
have to take PI as 22 by 7 so this would
be 22 by 7 which is equal to 44 into
seven divided by 2 into 20 2 so this is
2 into 22 again 22 22 gets cancel so
this is 7 centimeter therefore the
radius of the circle is 7 centimeters
also find its area now if we know radius
of a circle so this is now known as 7
centimeters so area would be PI R square
that is equal to 22 by 7 into 7 into 7
so the 7 and 7 will get cancelled 22
into 7 is 154 centimeters squared so
this is the area of the circle now if
the same wire is bent into the shape of
a square what would be the length of
so the same wire now is bent in the
shape of a square like this so we have
to find out the length of each side of
this square now the total length of the
wire still remains the same right and
the total length is 44 centimeters now
in this case this 44 centimeter would be
equal to the perimeter of the square
which is given by 4 into side so 4 into
L is equal to 44 centimeter therefore L
is equal to 44 by 4 which is equal to 11
centimeters therefore the side of the
length of each side of the square would
be 11 centimeters which figure encloses
more area circle or the square so area
of the circle we have already found this
154 centimeter square so in order to
compare the two areas we have to find
out the area of the square so area of a
square is given by the side into sign
that is length of one side multiplied by
length of neither side so length is
given as 11 so 11 into 11 is 121
centimeter square so if you compare 121
with 154 what do you see 154 is greater
therefore which encloses more area
therefore a circle encloses greater area
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