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The figure shows the shape of tunnel entrance. If the curved portion

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Bunuel
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The figure shows the shape of tunnel entrance. If the curved portion [#permalink] New post   25 Sep 2019, 04:49
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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. \(\frac{9\pi}{\sqrt{2}}\)


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The figure shows the shape of tunnel entrance. If the curved portion [#permalink] New post   25 Sep 2019, 05:24
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Bunuel wrote:

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. \({9\pi}{\sqrt{2}}\)

Show Spoiler
Attachment:
2019-09-25_1548.png


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
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Re: The figure shows the shape of tunnel entrance. If the curved portion [#permalink] New post   25 Sep 2019, 06:48
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Dillesh4096 wrote:
Bunuel wrote:

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. \({9\pi}{\sqrt{2}}\)

Show Spoiler
Attachment:
2019-09-25_1548.png


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


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?
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Re: The figure shows the shape of tunnel entrance. If the curved portion [#permalink] New post   25 Sep 2019, 08:32
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ayush19
given that curved portion is 3/4 i.e 3/4*360 ; 270*
so the part which is not curved would be 360-270 = 90*
Hope this helps.

ayush19 wrote:
Dillesh4096 wrote:
Bunuel wrote:

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. \({9\pi}{\sqrt{2}}\)

Show Spoiler
Attachment:
2019-09-25_1548.png


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


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?
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Re: The figure shows the shape of tunnel entrance. If the curved portion [#permalink] New post   25 Sep 2019, 12:32
Archit3110 thanks a lot. Got it now.
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Re: The figure shows the shape of tunnel entrance. If the curved portion [#permalink] New post   03 Sep 2023, 07:31
Hello from the GMAT Club BumpBot!

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Re: The figure shows the shape of tunnel entrance. If the curved portion [#permalink]
03 Sep 2023, 07:31
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