Latest Elitmus Aptitude Question SOLUTION: Q. Let a square of side ‘a’ inscribed in a circle having radius ‘r’ with center o. Now by assuming the side of circle as a diameter and drawn four smaller circle having ce

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(#M40152566) ELITMUS Numerical Ability question geometry Keep an EYE

Q. Let a square of side ‘a’ inscribed in a circle having radius ‘r’ with center o. Now by assuming the side of circle as a diameter and drawn four smaller circle having center o’. Now find the area of all four smaller circle which is outside from the bigger circle.

Asked In Elitmus niraj kumar (8 years ago)

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Deepak prajapati  (8 years ago)

Ans will be 2*(r)^2.
Exp:-Area of cirle O=pi*(r)^2 = pi*(r)^2.
Required area for one circle=(1/2)*Area of smaller circle - (area of segment made by larger circle - area of triangle made by larger circle)
=(pi*(r)^2)/4 - (pi*(r)^2)/4 + (r^2)/2
=(r^2)/2
so,for the four circle area will be=4*(r^2)/2
=2*(r)^2.

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Ankesh Verma  (8 years ago)

area of cirle O=pi*(1)^2 = pi

Nw the diameter of circle is also the diagonal of the square.
Hence each side of square will be sqrt(2).

=>Area of square=2

since each side of square is also the diameter of other 4 circles.
Hence summation of area of 4 circles=2*pi...........(1)

If u hav drwan its fig u'll find that to obtain the required ans u hav to subtract the area of 4 semi-circles formed on the side of the square from the each of the small portion outside the square.
To get that area of small portion =area of circle O-area of square =pi-2.......(2)

this small portion has to be substracted from the four semi-circles.
Hence, area of 4 semi-circles=2*pi/2= pi......[from (1)]
required ans=total area of 4 semi-circles - area of small portion(from (2))
=pi-(pi-2)
=2.

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imran alam  (6 years ago)

Ans=(area of square + area of small cirlcle which is outside of the square) - (area of bigger circle)
=(a^2 + ((4*pi*a^2 /4)/2) - pi*r^2)
=(a^2 + (pi*a^2 /2) - pi*r^2)
=(a^2 + (pi* (sqrt(2)*r)^2 /2) - pi*r^2) (since a=sqrt(2) *r)
=(a^2 + (pi*r^2 - pi*r^2)
=a^2

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swarup  (8 years ago)

@ankesh verma wrong answer..according to ur question answer should be a^2.But that is not the right question for ur answer..ur answer corresponds to this question :
The circle O having a diameter of 2cm, has a square inscribed in it.each side of the square is then taken as a diameter to form 4 smaller circles O'.find the total area of all four O' circles which is outside the cirle O.

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vishal  (8 years ago)

The ans is pi(r^2-a^2)

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kundan kumar mandal  (6 years ago)

Let, side of square = a
Radius of bigger circle = a / root 2
Radius of smaller circle = a/2
Area outside square = 4 * pi * (a/2)^2
area of secant outside square of bigger circle = 2pi - a;
Effective area =4*( 2*pi - (2*pi-a));
=4a;

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