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# If the center of a circle that has radius of 1 is located at random in

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Manager
Joined: 30 May 2018
Posts: 88
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
If the center of a circle that has radius of 1 is located at random in  [#permalink]

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06 Apr 2019, 01:10
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00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:44) correct 42% (01:55) wrong based on 26 sessions

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If the center of a circle that has radius of 1 is located at random in a rectangular region with dimensions 10 by 8, what is the
probability that the circumference of the circle will not exceed the rectangular region?

(A) 1/5
(B) pi/10
(C) 2/5
(D) pi/5
(E) 3/5
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If the center of a circle that has radius of 1 is located at random in  [#permalink]

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06 Apr 2019, 02:02
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1
MBA20 wrote:
If the center of a circle that has radius of 1 is located at random in a rectangular region with dimensions 10 by 8, what is the
probability that the circumference of the circle will not exceed the rectangular region?

(A) 1/5
(B) pi/10
(C) 2/5
(D) pi/5
(E) 3/5

For circle to remain contained within the rectangle, the centre must be kept at a distance of min 1 unit from boundaries of rectangle

i.e. Centre of the circle may lie within the rectangle of dimension (8-2) and (10-2) i.e. 6*8 region

Probability = favourable Region / Total region = 6*8 / 10*8 = 3/5

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If the center of a circle that has radius of 1 is located at random in   [#permalink] 06 Apr 2019, 02:02
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