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.

Jer,
I'm yet to go down the list to Mindrod's and Dej Mar's full comments, and acknowledge some failings in my perceptions.

When I first saw this I thought Calculus; I suspected this problem originated from class assignments, somewhere on site you alluded to such an area - I wonder if in my early maths such an intro would have made calc. easier for me to understand.

At this stage I've only looked at #1 seriously, cast a glance at #2, but I recognise this as a valuable teaching aide, especially if the volumetrics were in a '2D' rather than a '3D' senario as this.

Take 1.

Posted by brianjn on 2006-06-28 08:04:13