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.

(In reply to Solution to 7b using numerical integration by Charlie)

3.41655 cm agrees with Dej Mar's original estimate of 3.42 cm.  I'm probably at fault if Dej's subsequent revision is wrong, but I'd like to understand where I plugged in a bad value, or made a poor assumption.

Charlie, you said in your first post on 7B:

 "The angle that the axis of the cone makes with the bottom of the pot is atan(3/5); call the measure of this angle A. The angle that the opposing slant height makes with the bottom is 2A."

But wouldn't the angle that the opposing slant height makes with the bottom actually be 2*(90^o - A)?  Or am I drawing my picture wrong?

 

Edited on July 4, 2006, 12:34 am

Posted by Mindrod on 2006-07-04 00:28:14