Latest Elitmus Aptitude Question SOLUTION: The circle o having a diameter 2 cm,has square inscribed in it each side of the square is then taken as the diameter to form 4 smaller circles to\' find the total area of 4 circles

ans: 2 cm^2

draw diagram,

diameter of circle = diagonal of square = 2 cm
=> side of square = 2/√2 = √2 cm

each of 4 circles drawn have same radius = √2/2 = 1/√2 cm

area of 1 circle which is outside the circle 'O' = area of half circle - ( area of sector - area of traingle )

= 1/2 * pi * (1/√2)^2 - ( pi/4 - 1/2 *1 *1)

= 1/2 cm^2

so, total area of 4 circles which is outside the circle O = 4 * 1/2 = 2 cm^2

Since the square is inscribed in the circle,
diameter of circle = diagonal of square

===> diagonal of square = 2 cm
Side of square = diagonal/sqrt(2)= 2/sqrt(2) cm

Diameter of each of the 4 circles = 2/sqrt(2)
Radius of each of the 4 circles ,r = diameter/2 = 1/sqrt(2)

Total area of 4 circles = 4 * pi * r^2
=4 * pi * 1/2
=2*pi
=6.283cm^2

Dia.of circle o=2cm,therefore side of square=sqrt(2),
now,radious of small circle=sqrt(2)/2,
area of small circle=pi*{sqrt(2)/2}^2=pi/2cm^2
now ,half of outer area=pi/4cm^2
now area which are also included in circle o(segment )=area of sector-area of triangle={(pi/4)-(1/2)}cm2
therefore;
area of outer side from one side=pi/4-{(pi/4)-(1/2)}=1/2 cm^2
total area of outside of 4 side=4*1/2=2 cm^2....***2cm^2ans

ans: 2 cm^2

draw diagram,

diameter of circle = diagonal of square = 2 cm
=> side of square = 2/√2 = √2 cm

each of 4 circles drawn have same radius = √2/2 = 1/√2 cm

area of big circle(pi)- area of square(2) = area of all 4 sector made by side of square

area of 4 sector = pi - 2 = 3.14 - 2 = 1.14

required area = half area of all 4 small circle(4*0.5*pi/2) - area of all 4 sector(1.14)

required area = 3.14 - 1.14 = 2 cm^2

pls bhai if u really know the ans then clearly explain it or dont post ur answers

Ans. is 2*(pi-1)

2 cm2.Is right ans

The first thing I did was to find the side of the square inscribed in the circle,
as the diameter of the circle will be the diagonal of the square, this will form two 45 45 90 right triangles with a hypotenuse of 2.
Since s = ssqrt(2), 2 = s(sqrt(2).
divide 2 by sqrt(2) = 2/sqrt(2)
Multiply the numerator and denominator by sqrt(2) to obtain 2(sqrt(2)/2 for each side of the square, or sqrt(2)
Now, these are being used as diameters for four more circles, so we determine the radius of each one of the four to be sqrt(2)/2
So this value squared times pi will be the area of each circle, or 2/4 = 1/2 times pi = 1/2 pi for each circle times four circles results in 2 pi as the area for the four circles combined.

The area of the original circle is pi r^2, radius being 1 so the area of the original circle will come to 1pi.
So, since the outer circles obviously cover the original circle completely, the area outside the original should be 2pi minus pi, or one pi

its simply obvious that the diameter of the circle is the same as that the diagonal of the inscribed square
Here Firstly since the radius of the circle is 1.. the area of the circle is p.
Since the diagonal of the square is the diameter of the circle i.e. 2 so each side =sqrt(2)
=> Area of the square = 2

Now look closely we are asked to find out those areas of the smaller circles which is outside the bigger circle. So simply subtracting the area of the square area from the total area of the circle wont work actually. We also need to subtract the smaller portions of the large circle outside the circle. If you have any queries look at the diagram closely.

So firstly lets subtract the smaller portions of the large circle outside the circle which is ∏-2 right? [∏ being the area of the circle and 2 the area of the square] And wait………… (1)
Now lets look at the smaller circles each of which has a diameter of sqrt(2) and hence a radius of 1/sqrt(2)… And now look we are interested in only one half of the circle which is outside the square only. So the area of the half or semi-circle = [∏*[1/sqrt(2)]^2]/2=∏/4
Now there are 4 such semi circles we need to consider. i.e. the whole area = ∏/4*4=∏
Now simply subtract the area of the small portions of the large circle from the semi circles area to get our required area.
So the required area = ∏-(∏-2)=2

For these question area of 4 circle=squre area so ,diagonal =√2a=2=2 given
Area of square=2