Capthan wrote:

Considering a semicircular cross section of a one-way tunnel with a diameter of 20 feet. The single traffic lane is 12 feet wide and is equidistant from the side 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?

5 ½ ft

7 ½ ft

8 ½ ft

9 ½ ft

10 ft

B.

Here is why. (See attachment)

Let me know whether you cant see it. Hrmm maybe I cannot attach it... Owell. Here is my reasoning.

The line from the center of the semicircle is the same distance as the slanted line from the center of the semicircle.

This line is now Excluding the ½ foot. We now have 9 1/2feet as our hypotenous of the square. We get the square from the greater rectangle. Split the rectangle in two and we get a perfect square. (Assuming the entire semicircle is perfectly symmetrical).

Now we need the height of the rectangle or the height of our square. This is 9 ½ ft/sqrt2

~ 7 ½ ft