All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Cubes in a tin (Posted on 2006-05-15)
There is a rectangular tin 2cm by 3cm at the base, 2cm deep and open at the top.
It is filled with water to a depth of .4cm.
Twelve 1cm steel cubes are placed in the tin one by one. The first six form a single layer at the bottom. The next six form a second layer.

To what height does the water level rise after the placement of each cube?
Assume the cubes fit together tightly, leaving no spaces.

 See The Solution Submitted by Jer Rating: 2.6667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: this should be the solution | Comment 8 of 23 |
(In reply to this should be the solution by dominique)

"the volume is 0.4*3*2=2.4cm³

one cube is one cm³ added

so the new volume is after 1cube is 3.4cm³ (2.4cm³+1cm³)

divide this by 6 and you have the new height after one cube = 0.5666...cm"

For 6 times the new height to equal the volume of the water plus the volume of the cube, the cube could not extend above the height of the water--it must be the same 0.5666... cm.  But it can't be: it's solid and 1-cm high.

 Posted by Charlie on 2006-05-16 10:46:31
Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information