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Updated on: 19 Aug 2014, 03:10
Originally posted by PareshGmat on 18 Aug 2014, 22:01.
Last edited by PareshGmat on 19 Aug 2014, 03:10, edited 1 time in total.
Last edited by PareshGmat on 19 Aug 2014, 03:10, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (03:04) correct
38%
(03:09)
wrong
based on 107
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A dog is tethered to the corner of a rectangular shed. If the length of the rope is 5, and the shed has length 4 and width 3, what is the perimeter of the maximum area that is accessible to the dog? (The dog cannot enter the shed).
cowandrope_figure.PNG [ 1.62 KiB | Viewed 5200 times ]
a) \(7\pi + 8\)
b) \(8\pi + 8\)
c) \(8\pi + 9\)
d) \(9\pi + 10\)
e) \(\frac{17\pi}{2} + 10\)
Attachment:
cowandrope_figure.PNG [ 1.62 KiB | Viewed 5200 times ]
a) \(7\pi + 8\)
b) \(8\pi + 8\)
c) \(8\pi + 9\)
d) \(9\pi + 10\)
e) \(\frac{17\pi}{2} + 10\)
Looking at this image taken from the other thread, we see that we have 3/4 of the larger circle (radius 5) + 1/4 of the two smaller circles, one with radius 1, the other with radius 2.
That gives a total perimeter of \(10 \pi \frac{3}{4} + \frac{2 \pi}{4} + \frac{4 \pi}{4} = \frac{36 \pi}{4} = 9\pi.\).
Add the edges of the shed that the dog can also walk along, and the answer is \(9\pi +10\).
General Discussion
19 Aug 2014, 02:51
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PareshGmat
Similar question to practice: a-cow-is-tethered-to-the-corner-of-a-rectangular-shed-159700.html
It has been corrected now... 
