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25 Sep 2019, 04:49
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:15) correct
33%
(02:08)
wrong
based on 196
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Not Attempted Yet
The figure shows the shape of tunnel entrance. If the curved portion is 3/4 of a circle and the base of the entrance is 12 feet across, what is the perimeter, in feet, of the curved portion of the entrance?
A. \(9\pi\)
B. \(12\pi\)
C. \(9\pi \sqrt{2}\)
D. \(18\pi\)
E. \(\frac{9\pi}{\sqrt{2}}\)
Attachment:
2019-09-25_1548.png [ 3.04 KiB | Viewed 8874 times ]
25 Sep 2019, 05:24
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Bunuel
The base forms an Isosceles right angle triangle (45 - 45 - 90) with the center of the circle
Let r be the radius of the circle
Base corresponds to the side opposite to 90 deg
--> \(\sqrt{2}r = 12\)
--> \(r = 6\sqrt{2}\)
Perimeter of 3/4th of the circle = \(3/4*2π*6\sqrt{2}\)
= \(9π\sqrt{2}\)
IMO Option C
Pls Hit Kudos if you like the solution
25 Sep 2019, 06:48
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Dillesh4096
Could you please tell me, how do you know that the base forms a right angle at the center??
I know that it will form an isosceles triangle at the center, but how can we surely say that the angle subtended at the center is a right angle?
