Problem Set on Circles : 1 - Geometry of Quadrilaterals, Quantitative Aptitude Video Lecture | Study UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making - UPSC | Best Video for UPSC

the area of a circle is 24.6 four square
meters what is its circumference well
the formula for calculating the
circumference of a circle is equals to
two PI R and what is the formula for
calculating the area of a circle that's
PI R square right so area is 24 point 6
4 is equals to what is the value of pi
it is 22 by 7 times R square so R square
is equals to 24 point 6 4 divided by 22
times 7 solving this you will get the
value as 7 point 8 4 R square is equal
to 7 point 8 4 taking the underhook on
both the sides you get R is equals to if
you calculate the under root of 7 point
8 4 it will come out as 2.8 now that you
know the radius of the circle you can
calculate its circumference so
circumference is equals to 2 into pi is
22 by 7 times r is 2.8 right now seven
times zero point four is equal to two
point eight so you have zero point four
times two that's point eight times 22 so
this is seventeen point six meters so
that's the circumference so option C is
the correct answer
a cow is thethird in the middle of a
field with 14 feet long rope if the cow
grazes 100 square feet per day then
approximately what time will be taken by
the cow to grace the whole field well
the cow will graze a circular area and
the radius of that circular area will be
the length of the rope and that's 14
feet now let us calculate the area of
this circle so area is equal to PI R
square so pi is 22 by 7 times r is 14 so
14 times 14
7 times 2 is 14 22 times 2 is 40 4 times
14 and that is equal to 616 square feet
now this is the area I mean the total
area grazed by the cow now we have been
given that the cow grazes 100 square
feet per day and we have been asked how
many days will be required to completely
graze this total area of 616 square feet
so the number of days required will be
equal to the total area divided by the
area grazed in one day so 616 by hundred
and that's equal to six point one six so
approximately it is equals to six days
right so the time taken to graze is six
days option B the difference between the
circumference and the radius of a circle
is 37 centimeters what is the area of
this circle well we have been given the
difference between the circumference and
the radius and that's 37 well what is
the formula for circumference that is 2
PI R so 2 PI R minus R on the left hand
side we have and on the right hand side
we have 37 right so if I take our common
I get 2 pi minus 1 okay is equals to 37
and that is R into 2 pi is 2 into 22 by
7 that's 44 by 7 minus 1 is equal to 37
so R times 44 minus 7 by 7 so 44 minus 7
is 37 by 7 is equal to 37 so this gets
cancelled out R is equal to 7 now we
found out the radius we have to find out
the area so area is equal to PI R square
that's 22 by 7 times 7 times 7 this gets
cancelled out we have 22
times seven and that is equals to 154
and the unit is centimeter square so
option C is the correct answer a
circular wire of radius 42 centimeters
is bent in the form of a rectangle whose
sides are in the ratio of 6 is to 5
what is the smaller side of the
rectangle so there is a circle and there
is a rectangle and we have been given
the ratio of the sides of this rectangle
that 6 is 2 pi so I can write it as 6 X
+ 5 X X being the constant now we have
been given the radius of the circular
wire that's 42 centimeters now it is
said that this circular wire is bent in
the form of rectangle that means the
perimeter of the circle will be equal to
the perimeter of the rectangle in other
words the circumference of the circle is
equals to the perimeter of the rectangle
so C is equals to P what is the formula
to calculate the circumference of a
circle that's 2 PI R it is equals to
perimeter is 2 times L plus P so 2 times
6x plus 5 X okay so we have 2 into 22 by
7 times radius is 42 is equal to 2 into
5x plus 6x that's 11 X this 2 and this 2
gets cancelled out 7 times 6 is 42 so
you have 22 times 6 is equal to 11 X now
this 11 comes to the left so we have X
here and 11 here 11 times 2 is 22
therefore X is equal to 6 times 2 that
is 12 so the value of x is 12 what has
been asked what is the smaller side of
the rectangle and that is 5x so it will
be equals to 5 times 12
that's 60 centimeter so option D is the
correct answer if the ratio of the areas
of two circles is four is to nine then
what is the ratio of their circumference
--is well the ratio of the circumference
s will be C 1 by C 2 and that will be
equals to 2 pi R 1 upon 2 pi R 2 right
so these two PI's and 2pi sets cancelled
out we have the ratio of the
circumference s as r1 by r2 ok now let
us find out what is r1 by r2 well to
find that out we have been given the
ratio of the areas so a1 by a2 is given
as 4 by 9 well what is a 1 by a 2 well
it is PI R 1 square divided by PI R 2
square and that's 4 by 9 pi n pi gets
cancelled out you have R 1 square by r2
square it is equals to 4 by 9 now taking
the under root in both the sides of
equal to you get this so if you solve
this you will get r1 by r2 and that's
root 4 is 2 root 9 is 3 so put this here
so you get the ratio of the
circumference s as 2 by 3 so option a is
the correct answer