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Children playing a game roll a circular disc to see who can roll it th

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Bunuel
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Children playing a game roll a circular disc to see who can roll it th [#permalink] Children playing a game roll a circular disc to see who can roll it th   29 Aug 2018, 03:49
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Children playing a game roll a circular disc to see who can roll it the farthest. What is the area, in square centimeters, of the disc they are playing with?

(1) One child rolled the disc exactly 540 degrees and it rolled exactly 6π centimeters.
(2) On one roll the disc traveled for 6 complete rotations, which lasted a total of 10 seconds.
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sumit411
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Re: Children playing a game roll a circular disc to see who can roll it th [#permalink] Children playing a game roll a circular disc to see who can roll it th   29 Aug 2018, 05:57
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Bunuel wrote:
Children playing a game roll a circular disc to see who can roll it the farthest. What is the area, in square centimeters, of the disc they are playing with?

(1) One child rolled the disc exactly 540 degrees and it rolled exactly 6π centimeters.
(2) On one roll the disc traveled for 6 complete rotations, which lasted a total of 10 seconds.
Basically we are asked about the radius of the disc. If we know the radius, we know the area

St1) We know one rotation covers 2*pi*r distance and we know the number of rotations. So we can equate that distance by 6pi

We can find radius.
Sufficient

St2) only thing we can know is velocity that is of no use to find radius.
Insufficient

IMHO answer is A

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Children playing a game roll a circular disc to see who can roll it th [#permalink] Children playing a game roll a circular disc to see who can roll it th   29 Aug 2018, 06:43
Bunuel wrote:
Children playing a game roll a circular disc to see who can roll it the farthest. What is the area, in square centimeters, of the disc they are playing with?

(1) One child rolled the disc exactly 540 degrees and it rolled exactly 6π centimeters.
(2) On one roll the disc traveled for 6 complete rotations, which lasted a total of 10 seconds.


Question stem:- Area of disc=?
We require radius of disc.

St1:- One child rolled the disc exactly 540 degrees and it rolled exactly 6π centimeters.
540 degree=360 degree(one complete rotation)+180 degree(Half rotation)=6π
Or, Rolling distance at 540 degree=Rolling distance at one complete rotation+Rolling distance at Half rotation=\(2*\pi*r\)+\(\pi*ri\)=6π
(1 complete rotation is equivalent to a distance of \(2*\pi*r\))
Or, \(3*\pi*r\)=6π Or r=2
Hence area can be determined.
Sufficient.

St2:- On one roll the disc traveled for 6 complete rotations, which lasted a total of 10 seconds.
We need info on distance traveled by the disc in one rotation or 6 rotations in in order to determine radius . Time has no function here.
Insufficient.

Ans. (A)
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Children playing a game roll a circular disc to see who can roll it th [#permalink]
29 Aug 2018, 06:43
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Bunuel
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