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Rising water levels (Posted on 2006-06-26) Difficulty: 4 of 5
You have rectangular pot of water 10cm by 10cm at the bottom and 6 cm deep. It is filled to a depth of 3cm.

You have 7 solid steel shapes in front of you. The question is to find the new level of the water after each shape is put in the pot in the orientation described. The previous shape is removed before adding the next.

1. A cube 5cm on a side.

2. A prism in the shape of a right triangle with legs 5cm long. It is 5cm high but is placed on one of its legs with its hypotenuse sloping out of the water.

3. Another prism, this one having an equilateral triangle of sides 5cm and height 5cm. It is to be placed on its side with two faces sloping up out of the water.

4. A regular hexagonal prism. Each edge of the hexagon is 4cm and the height is 5cm. It is to be placed on its side.

5. A right square pyramid. Its base is 6cm on a side. It is 5cm high. It is to be placed base down.

6. A right cylinder of radius 3cm and length 5cm. It is to be placed on its side.

7a. A right cone of radius 3cm and height 5cm. It is to be placed base down.

7b. The same cone as 7a. This time placed on its side.

No Solution Yet Submitted by Jer    
Rating: 4.1667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution to 7b using numerical integration Comment 26 of 26 |
(In reply to Solution to 7b using numerical integration by Charlie)

Charlie, It took me a while to figure out your program, but I can't find anything wrong with it.  So, I must have made an error in some part of my calculation.   (Nice program, by the way.)

I'm using an Excel spreadsheet do perform my numerical analysis.  I'm having a hard time seeing where I might have mistyped a formula, but the mistake must be in there somewhere.

Thanks for your input on this problem.  I'm having fun relearning Trigonometry. 


  Posted by Mindrod on 2006-07-06 00:33:13
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