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IMAGE.JPG The figure above shows the dimensions of a [#permalink] New post 04 Sep 2008, 07:33
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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
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Re: tunnel [#permalink] New post 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



radius =10
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: tunnel [#permalink] New post 04 Sep 2008, 07:53
B should be the answer. Suresh beat me to it, though ;;)
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Re: tunnel [#permalink] New post 10 Sep 2008, 04:46
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



radius =10
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: tunnel [#permalink] New post 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



radius =10
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


your are right. thanks
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Re: tunnel [#permalink] New post 10 Nov 2011, 03:07
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
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tunnel.JPG
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Re: tunnel   [#permalink] 10 Nov 2011, 03:07
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