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 Rising water levels (Posted on 2006-06-26)
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(3): answers (spoiler) - some over sight? | Comment 4 of 26 |
(In reply to re(2): answers (spoiler) - some over sight? by Trevor)

In my last comment I noted that you have to account for rising height as the object is immersed.  In the first case the object had a uniform shape and so the water level was displaced in a lineal fashion.

The profile of each ensuing shape needs to be considered.
Note with the right triangular prism will displace less water in its 2cm of immersion than in its first.  I expect that there is an easy calculus solution to all of these, but you may still get there via normal geometric volumes and pencil and paper.

 Posted by brianjn on 2006-06-27 22:24:13

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