In the figure ,small circel with radius r intersects larger

Question

circles.png In the figure, small circel with radius r intersects larger circle with radius R (R>r). If k>0, what is the difference in the areas of the non overlapping parts of two circles? (1) R=r+3k (2) kR/(kr-6)=-1

Bunuel · Accepted Answer

Look at the diagram: Circles.JPG We are asked about the difference between the areas of green and yellow regions. {Green}={Big circle} - {Red} and {Yellow}={Small circle} - {Red} , so, as you can see we should subtract red region (x) from the areas of both circles. Difference between the areas will be: {Green}-{Yellow} = ({Big circle} - {Red}) - ({Small circle} - {Red}) = {Big circle} - {Small circle} . Hope it's clear.

subhashghosh · Answer

Area 1 = OVerlap + ( pi*r^2 - Overlap)

Area 2 = OVerlap + ( pi*R^2 - Overlap)

So ( pi*R^2 - Overlap) - ( pi*r^2 - Overlap) = ?

= pi(R-r)(r+R)

(1)

R-r = 3k

Insufficient

(2)

kR = -kr +6

=> r+R = 6/k

Insufficient

(1) + (2)
So difference = pi* 3k * 6/k = 18pi

Answer - C

What is the OA ?

amit2k9 · Answer

C1-C2 = pi* (R^2-r^2)

a. R=r+3k does not give R+r value.

b really not sure what this option says is it (kR/kr) = 5 then R/r = 5. not sufficient.

a+b 5r = r+3k gives 4r = 3k. 
substituting in original equation gives area in terms of k.

Hence not sufficient. E.

PS: option B has to be mentioned clearly.

subhashghosh · Answer

@amit2k9, I think (2) should say :
(kR) / (kr – 6) = -1

@AnkitK, please confirm if what I've suggested is correct.

Spidy001 · Answer

Let x be the overlapping area.

we were asked find difference in non overlapping areas =  (pi*R^2-x)-(pi*r^2-x)

= pi*(R^2-r^2) = pi*(R+r)*(R-r)

1. Not sufficient.

we only know R-r ,not R+r.

2. Not sufficient

kR/(kr-6) = -1 
 => R+r = 6/k. but we dont know R-r

Together, its sufficient.

= pi*(R+r)(R-r) = pi*(6/k)(3k) = 18pi.

Answer is C.

AnkitK · Answer

@subhashghosh:I regret the delay caused .OA is C only.Yes your approach is correct.

garimavyas · Answer

yes , the explanation is a decent one. 
we have (R-r) from 1 and (R+r) from 2. if we can eliminate the overlapped area from the equation , the question is solved. 
So C is the answer.

hussi9 · Answer

Good Question ..
I assumed that solving both equation will give answer in terms of K so chose E. 
Rather careless way of thinking...

hussi9 · Answer

Good Question ..
I assumed that solving both equation will give answer in terms of K so chose E. 
Rather careless way of thinking...

rohitgoel15 · Answer

I have one question in the above explanation.

Shouldnt x be deducted only once in the equation ?? .. 
 (pi*R^2-x)-(pi*r^2-x) --> (pi*R^2)-(pi*r^2) - x

jlgdr · Answer

What does 'k' stand for in the question stem?

Bunuel · Answer

k is just some number.

bumpbot · Answer

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In the figure ,small circel with radius r intersects larger

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