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Suppose the areas of the two sectors shown are equal, what is the rati

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Suppose the areas of the two sectors shown are equal, what is the rati  [#permalink]

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Suppose the areas of the two sectors shown are equal, what is the ratio of angle a to angle b?


(1) The ratio of the radius of circle A to that of circle B is 3 : 1.

(2) The ratio of the area of circle A to that of circle B is 9 : 1.



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Attachment:
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image012.jpg [ 2.59 KiB | Viewed 261 times ]

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Re: Suppose the areas of the two sectors shown are equal, what is the rati  [#permalink]

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New post 11 Sep 2018, 03:17
Bunuel wrote:
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Suppose the areas of the two sectors shown are equal, what is the ratio of angle a to angle b?


(1) The ratio of the radius of circle A to that of circle B is 3 : 1.

(2) The ratio of the area of circle A to that of circle B is 9 : 1.



Attachment:
image011.jpg

Attachment:
image012.jpg


Ratio of areas = \(angle_1 * r_1^2 / angle_2 * r_2^2\)

now we know that \(angle_1 * r_1^2 = angle_2 * r_2^2\) because ratio of area is 1 as bopth are equal

hence, \(angle_1 / angle_2 = r_2^2 / r_1^2\)

So we need to know only the ratio of the radius


Question : FInd ratio of angles of the two sectors?

Statement 1: The ratio of the radius of circle A to that of circle B is 3 : 1.

SUFFICIENT as per the above reasoning mentioned

Statement 2: The ratio of the area of circle A to that of circle B is 9 : 1.

Ratio of area is same as square of ratio of radius which is needed to answer the question hence

SUFFICIENT

Answer: option D
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Re: Suppose the areas of the two sectors shown are equal, what is the rati &nbs [#permalink] 11 Sep 2018, 03:17
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Suppose the areas of the two sectors shown are equal, what is the rati

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