Latest Elitmus Aptitude Question SOLUTION: a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out t

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(#M40157719) ELITMUS Numerical Ability question geometry Keep an EYE

a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles?
asked in elitmus on 16 october.

Asked In Elitmus vikas rai (7 years ago)

Unsolved Read Solution (6)

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CHANPREET SINGH  (7 years ago)

Let radius of circles be r.
When 4 circles are drawn using the corners of the square,then it forms 4 quadrants inside the square.

We can obtain the relation,
r + 2r + r = diagonal of square
(radius of quadrant at corner) + (diameter of circle at centre of square) + (radius of quadrant at diagonalled corner) = length of diagonal

4r=2 * Root2
r=1/Root2

Area left = Area of square - Area of circle at centre - Area of 4 quadrants
= (2*2) - (pi * square(1/Root2)) - (4*(1/4)*pi*square(1/Root2))
= 4-(pi/2)-(pi/2)
= 4-pi
= 4-3.14 = .86 sq units

Is this solution Helpfull? Yes (21) | No   

priyadarshan kumar  (7 years ago)

let the radius of circle is 'r'

area of the circle which is at corner = (22/7*r^2)/4
hence the area of all four circles are = 22/7*r^2
areaof circle which is made on center of suare is = 22/7*r^2

total area of all circles are = 2*22/7*r^2...........................(1)

if we construct the diagram we get the relation

4r = 2sqrt2
r = 1/sqrt2

put the value of r in eqn 1 and we get

2*22/7*1/2 = 22/7 = 3.14

area of suare = 2^2 = 4
area of remaining part = 4-3.14 = 0.86

Is this solution Helpfull? Yes (7) | No (6)  

Pawan Pandey  (7 years ago)

4-2.pie r^2 sq-units.

Is this solution Helpfull? Yes (1) | No (2)  

AMIT KUMAR  (7 years ago)

science there is given there are 4 circles on the corner and one in center
which means, diameter of center's circle+sum of redius of two circles = digonal of square
2r+r+r = 2root2
r=1/root2

therefor,
requred area = area of square - 4*pi/4*r^2 - pi*r^2 (sciene corner's sectors make angle of 90degree)
=4 - pi/2 - pi/2
=4 - pi
=4 - 3.14
=0.86 square unit

Is this solution Helpfull? Yes (1) | No   

SHAVALA NANDEESHWARUDU  (7 years ago)

Area of Square=1 sq.units
By combining the four corner quarter circles,we can form one full circle of radius 1
Area of four quarters=(22/7)*1=22/7=3.14 sq.units
The area not covered= Area of Square-Area of circle=4-3.14=0.86 sq.units (approx)

Is this solution Helpfull? Yes | No (3)  

pooja kumari  (7 years ago)

ans: 3*(1-pi/4)

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