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Question 1120549: A park has a water channel with a semicircular cross section that has a diameter of 13ft. The boats that are going to be used in this water sytem have a rectangular cross sections and are known to submerge 3ft into the water. If the water channel is to be filled with water 6.5ft deep, what is the possible maximum width of the boats?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Assuming the boats will be centered in the channel, the width of the boat will be 2x, where x is the other leg of a right triangle with one leg 3 (the depth of the boat in the water) and hypotenuse 6.5 (the radius of the semicircular channel.
However, I wouldn't bother going any further with the calculations, because you have a problem.
If the diameter of the channel is 13ft and is filled with water 6.5ft deep, then the channel is full; if you put any boats in the channel you are going to have a flood.
Perhaps you have misstated the problem...?
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No; I can't help you "rephrase" the problem, because it doesn't make sense. The numbers you show simply don't make sense.
If you are showing the problem EXACTLY as it was given to you, then it makes no sense, and you can't do anything with the problem.
More likely, the numbers you have shown are not the correct numbers.
Perhaps the channel has a RADIUS of 13ft instead of a DIAMETER of 13ft? Then filling it to a depth of 6.5ft would make sense.
Answer by ikleyn(52799)  (Show Source):
You can put this solution on YOUR website! .
The GIVEN part is THIS :
1) The channel is a semicircle in the cross section with the diameter of 13 m and the radius of 6.5 m. It is filled up to the upper level.
2) The boats are submerged 3 ft into the water.
3) The boat has / (the boats have) the width 2x.
The question is :
Find the maximum possible x and then 2x (assuming that the boat is centered along the channel axis).
Solution
x =  = 5.77 ft.
2x = 2*5.77 = 11.53 ft.
Answer. The maximal width of the boat is 11.53 ft.
Solved.
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