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# The figure above shows the dimensions of a semicircular cros

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Senior Manager
Joined: 02 Dec 2007
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The figure above shows the dimensions of a semicircular cros [#permalink]

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04 Sep 2008, 07:33
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Difficulty:

65% (hard)

Question Stats:

54% (01:01) correct 46% (00:39) wrong based on 343 sessions

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The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5½ ft
B. 7½ ft
C. 8 ½ ft
D. 9½ ft
E. 10 ft

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-figure-above-shows-the-dimensions-of-a-semicircular-100337.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jul 2014, 02:23, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.

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Re: The figure above shows the dimensions of a semicircular cros [#permalink]

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04 Sep 2008, 07:49
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Nihit wrote:
Attachment:
IMAGE.JPG

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel(dia= 20 ft). The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5½ ft
B. 7½ ft
C. 8 ½ ft
D. 9½ ft
E. 10 ft

Say AOB is base of the semi circle.
points X and Y are on edges of the traffic lane (XY=12)
OX=6

Find the height perpendicular to X and touches the semi circle.
= sqrt (6^2+10^2) =8

we need 1/2 ft clearance.

so height must be (8-1/2) =71/2 ft

B.
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Re: The figure above shows the dimensions of a semicircular cros [#permalink]

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04 Sep 2008, 07:53
B should be the answer. Suresh beat me to it, though ;;)
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Re: The figure above shows the dimensions of a semicircular cros [#permalink]

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10 Sep 2008, 04:46
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x2suresh wrote:
Nihit wrote:
Attachment:
IMAGE.JPG

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel(dia= 20 ft). The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5½ ft
B. 7½ ft
C. 8 ½ ft
D. 9½ ft
E. 10 ft

Say AOB is base of the semi circle.
points X and Y are on edges of the traffic lane (XY=12)
OX=6

Find the height perpendicular to X and touches the semi circle.
= sqrt (6^2+10^2) =8

we need 1/2 ft clearance.

so height must be (8-1/2) =71/2 ft

B.

Minor correction:
The height perpendiculr to X and touches the semi circle
=sqrt (10^2 - 6^2) = 8

Kudos [?]: 104 [2], given: 0

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Re: The figure above shows the dimensions of a semicircular cros [#permalink]

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10 Sep 2008, 06:02
dancinggeometry wrote:
x2suresh wrote:
Nihit wrote:
Attachment:
IMAGE.JPG

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel(dia= 20 ft). The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5½ ft
B. 7½ ft
C. 8 ½ ft
D. 9½ ft
E. 10 ft

Say AOB is base of the semi circle.
points X and Y are on edges of the traffic lane (XY=12)
OX=6

Find the height perpendicular to X and touches the semi circle.
= sqrt (6^2+10^2) =8

we need 1/2 ft clearance.

so height must be (8-1/2) =71/2 ft

B.

Minor correction:
The height perpendiculr to X and touches the semi circle
=sqrt (10^2 - 6^2) = 8

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Re: The figure above shows the dimensions of a semicircular cros [#permalink]

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10 Nov 2011, 03:07
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Why are we considering only the line perperndicular to X? Why not another line can be 3 feet away from both sides of the traffic lane?

What am I doing wrong?

Refer attached diagram
Attachments

tunnel.JPG [ 14.54 KiB | Viewed 27955 times ]

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Re: The figure above shows the dimensions of a semicircular cros [#permalink]

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23 Jul 2014, 02:18
because the limiting case is case 1 as shown in the diagram ...

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Re: The figure above shows the dimensions of a semicircular cros [#permalink]

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23 Jul 2014, 02:24
10
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Expert's post
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Nihit wrote:

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5½ ft
B. 7½ ft
C. 8 ½ ft
D. 9½ ft
E. 10 ft

See the diagram attached:

Rectangle inscribed has the length of traffic lane 12. So max height of vehicle will be 1/2 foot less than the width of this rectangle.

Now, let O be the center of the semi-circle, then OA=radius=20/2=10 and OB=12/2=6 --> $$AB=\sqrt{OA^2-OB^2}=\sqrt{10^2-6^2}=8$$.

So max height of the vehicle that are allowed to use the tunnel is 8-0.5=7.5.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-figure-above-shows-the-dimensions-of-a-semicircular-100337.html
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Re: The figure above shows the dimensions of a semicircular cros   [#permalink] 23 Jul 2014, 02:24
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# The figure above shows the dimensions of a semicircular cros

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