Latest Elitmus Aptitude Question SOLUTION: A circle O having the diameter of 2 cm, has a square inscribed in it.Each side of square is taken as diameter to form 4 smaller circles OO''.Find the total area of all the four OO

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(#M40018458) ELITMUS question Circle Keep an EYE

A circle O having the diameter of 2 cm, has a square inscribed in it.Each side of square is
taken as diameter to form 4 smaller circles OO''.Find the total area of all the four OO' circles which is outside the circle O
Options a)2 B)pi-2 C)2-pie/4 D)2-pie/2

Asked In Elitmus Sumit Rawal (11 years ago)

Unsolved Read Solution (7)

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sivaraman  (11 years ago)

area of circle O= 22/7*(1^2)=22/7 sq.cm
side of square=2^1/2 * a
here diagonal length=2. so a=2^1/2 cm
area of square =a^2=2 sq.cm
area of one smaller circles=(22/7)*2 sq.cm
area of one smaller circle outside circle O=((22/7)*2)/2-8/28 sq.cm
area of 4 smaller circle=22/7-8/7=14/7=2 sq.cm

Is this solution Helpfull? Yes (9) | No (3)  

Saiyam Behl  (10 years ago)

area of cirle =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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DIKSHA RANGNANI  (10 years ago)

when i solved i got pi as answer
help

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Ravindra  (10 years ago)

yeah diksha i have also got the pi

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Nani  (10 years ago)

correct ans is 2

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arvind  (10 years ago)

can any one tell me how is it becomes 2 because we have to find the area of circle OO" which is outside of the circle O not out side of square..

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anand agarwal  (9 years ago)

area of large circle = pie
area of square is 2
now,take 1 smaller circle and
calculate area of half of circle = pie/4
next calculate (area of circle -area of square)/4===(pie-2)/4
now area of 1 circle outside the circle = pie/4-[(pie-2)/4]===1/2
now we get area of 1 circle which is outside from circle hence multiply by 4 we get 1/2*4=2

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