Examples: Circumference and Area of Circle (Part- 2) Video Lecture - Class 7

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question number 4 a circular flower
garden has an area of 314 meters where a
sprinkler at the center of the garden
can cover an area that has radius of 12
meters will the sprinkler water the
entire garden let let's again make use
of a diagram to understand the problem
so let's say that there is a circular
flower garden something of this sort
okay and the total area of this flower
garden is given as 314 meter square so
area of the garden is 314 meter square a
sprinkler at the center of the garden so
you have a sprinkler here at the center
of the garden and the sprinkler what
what does the sprinkler do a sprinkler
spreads water you know gives water to
the plants which is there in the garden
so it is located at the centre and this
sprinkler can cover an area that has
radius of 12 meters right so now we have
to find out how much area does the
sprinkler covers because only the radius
of the area is given so area that
sprinkler covers would be PI R square
and an is given as 12 meters 2 so 5 PI
into 12 into 12 that is 144 into 3.14
which is equal to 450 2 point 1 6 meter
square so this is the area that the
sprinkler covers now when you look at it
you see this is the area area of the
garden is 314 meters sprinkler is
located at the centre that means the
sprinkler would also sprinkle water
equally in all direction now as per our
calculation the water that the area that
the sprinkler would cover is 452 0.16
square which is a larger area than that
of the garden so the sprinkler then the
water from the sprinkler can actually
reach even outside the garden so the
question is will the sprinkler what are
the entire garden yes of course it will
water then thank garden that's because
its water is capable of reaching even
beyond the garden so obviously it will
be able to sprinkle the entire garden
question number five how many times a
wheel of radius 28 centimeters must
rotate to go 352 meters okay so when you
look at a wheel this is a wheel so when
you look at this wheel how does the
wheel rotate now let's see now as we I
mentioned before so one complete
rotation of the wheel it would actually
mean the circumference of the wheel that
is one complete rotation so one complete
rotation what does that actually means
in one complete rotation of the wheel it
covers a distance which is equal to the
circumference of the wheel so distance
covered will be equal to circumference
of the wheel right because in one if you
start from this point so by the time it
covers this much distance that is
nothing but the circumference of the
wheel right so in one root so what is
the circumference of this V let us first
find out the circumference of the wheel
so for this particularly if the
circumference would be 2 PI R that is 2
into 22 by 7 into August 28 centimeters
so this is equal to 7/4 or 28 so this
would be 44 into 4 which is equal to 176
so this is 176 centimeters now here the
distance is given in meters so let us
convert this also in beaker so 176
divided by 10 meters switches sorry
divided by hundred meters which is one
point seven six meters so this is the
circumference of the wheel so now to
cover one point seven six meters the
number of rotation how many times the
wheel rotates the wheel rotates one time
because it was just one rotation with
where it covers a distance equal to the
circumference that means to cover this
much distance that is the circumference
it rotates one time therefore to cover
352 meters how many times it would
rotate it would rotate 352 divided by
one point seven six so now when you
calculate this it comes out to be 200
therefore it needs to rotate for 200
times in order to cover 352 meters thank
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