Latest Elitmus Aptitude Question SOLUTION: a ring having radius 2 units is placed in the corner of a room such that it touches the adjecent walls. if a smaller circle is drawn in between the ring and the corner point of the

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Geometry

Elitmus Question Papers:

(#M40157009) ELITMUS Numerical Ability question geometry Keep an EYE

a ring having radius 2 units is placed in the corner of a room such that it touches the adjecent walls. if a smaller circle is drawn in between the ring and the corner point of these two walls, what would be the area of such a circle? i dont remember the options...asked in elitmus on 10/07/2016

Asked In Elitmus abhishek chaubey (7 years ago)

Unsolved Read Solution (22)

Is this Puzzle helpful?   (8)   (0) Submit Your Solution Geometry

Read Solution (22) :

Abhay choudhary  (7 years ago)

when the circle is touching the wall and radius is 2 unit, then the gap between the circle and wall forms a square with side of 2 unit.... so we have to find the diagonal of the square which is D^2=2^2+2^2 =2.8284.
so if we subtract 2.8284 -2=0.8284 ... the new circle having a diameter of 0.8284 and RADIUS will be 0.4142
by solving we have πr2 =0.53919373

Is this solution Helpfull? Yes (8) | No (10)  

abhishek chaubey  (7 years ago)

no one is considering here the gap between peripheri of smaller circle and the corner point...as a matter of fact a circle cant touch corner of a wall unless its radius is zero...means a point. and yeah ...i remebered options too now...
a) root2-1 ...which is indeed 200% wrong coz of ignoring abovesaid distance
b) 3-2*root2 c) 6-4root2 d)7-4root 2
now think again....

Is this solution Helpfull? Yes (6) | No   

sangeeta kumari  (7 years ago)

answer will be pi*(6-4root2)^2

Is this solution Helpfull? Yes (6) | No (1)  

Piyush Sinha  (7 years ago)

Method1:
Area of circle =4pi, Area of Sector of Circle =pi
Area of square =2*2=4
Area enclosed can be dertemined = Area of Square - area of sector .
Method 2;
Radius of Circle =2
Diameter of Square =2root2
hence diameter of small circle= 2root2- 2=0.82
radius of circle =0.82/2=0.41
hence area of small circle=pi *0.41*0.41=Ans

Is this solution Helpfull? Yes (5) | No (3)  

Shashank Gupta  (7 years ago)

pi*[root(2)-1]^2

Is this solution Helpfull? Yes (4) | No   

sushama singh  (7 years ago)

2(root2 - 1)
x= ______________
(1 + root2)

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

Deepak singh  (7 years ago)

Draw lines from centre of ring to corner lines I.e perpendicular.
Draw a line from centre of smaller circle to radius of bigger ring....
It will be more clear from figure...
Equation will be
(2-x)^2+(2-x)^2=(2+x)^2
Solve u will get 6-4√2

Is this solution Helpfull? Yes (2) | No   

Naveen babu  (7 years ago)

its devastating my mind

Is this solution Helpfull? Yes (1) | No   

ashtosh  (7 years ago)

taking radius os small circle as r. in that case pythagores theorem will be applied where hypotenuse will be (2+r) and other two sides are (2-r) and (2-r) equate both side and solve for r you will get the solution.

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

sachin pratap singh  (7 years ago)

option b is correct

Is this solution Helpfull? Yes (1) | No   

PRANJAL PANDEY  (6 years ago)

Let r be the smaller radius and x be the gap between smaller circle and corner. Now,
Length of diagonal of square formed due to bigger circle=2root2
2root2= 2+2r+x (as bigger radius=2)
further, 2(root2 -1)= 2r+x
now apply pythagoras theorem to find the distance between center of smaller circle to corner(r+x).
Here we get, r+x = 2(r^2)
Now we already have 2r+x,
So r+r+x=2(root2 -1)
On simplifying for value of r, we get r=6-4root2

Is this solution Helpfull? Yes (1) | No   

Subhrata Patra  (7 years ago)

radius of smaller circle= 2(root2-1)/2= (root2-1)

Is this solution Helpfull? Yes | No (2)  

abhishek chaubey  (7 years ago)

sorry....these options are corresponding to radius of smaller circle bt i hv asked area for the same in question....so apologize fr it ...u guys solve it fr radius..

Is this solution Helpfull? Yes | No (2)  

SAKSHI  (7 years ago)

How did u guys solve it?

Is this solution Helpfull? Yes | No   

shubham vinod patil  (7 years ago)

let 'a' be the radius then,
a+a*root(2)=0.828

Is this solution Helpfull? Yes | No (1)  

Ritesh Seth  (7 years ago)

In this question how can we find the side of square. There is nothing given for square side . when i found the side of the square then i will solve this question

Is this solution Helpfull? Yes | No   

AVINESH KUMAR  (7 years ago)

radius will be 6-4root2
and area of small circle will be Pi*6-4root2

Is this solution Helpfull? Yes | No   

Pawan kumar  (7 years ago)

let the radius of smaller circle 'r'.
By applying pythagoras theorem we find the gap occur b/w wall &smaller circle [since wall act like tamgent to circle]

rsqrt2+r+2=2sqrt2
by solving this we get r=6-4sqrt2

Is this solution Helpfull? Yes | No   

pooja kumari  (7 years ago)

distance from corner point to peripheri= 2*root2-2
radius of smaller circle= 2*(root2-1)/root2+1
area =pi*r2

Is this solution Helpfull? Yes | No   

deepak saroha  (7 years ago)

π4((3-2√2)/(3+2√2))

Is this solution Helpfull? Yes | No   

intakhab  (6 years ago)

radius is 3-2root(2)
area is {17-12root(2)}*3.14

Is this solution Helpfull? Yes | No   

rohan  (5 years ago)

let dia of smaller circle be =d
length of diagonal from the centre of the bigger circle to the corner of the wall= sqrt(8).
distance from the corner to the tip of smaller circle = a.
using similarity,
2/sqrt(8)=d/2/(d/2+a).......(2)
a = sqrt(8) - d - 2...............(1)
solving the eqn. we will get the value of d, and hence the area.

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.