Hello, Mars!
A rectangular fish tank has a base 2 feet wide and 3 feet long. When the tank is
partially filled with water, a solid cube with an edge length of 1 foot is placed in the tank.
If no overflow of water from the tank is assumed, by how many inches will the level of
the water rise when the cube becomes submerged?
We can talk our way through this problem.
The original volume of water looks like this:
Code:
*-----------*
/ /|
/ / |
/ / |
*-----------* *
| | /
h| | /2
| |/
*-----------*
3
This block of water has: width 2 feet, length 3 feet, height feet.
The volume is: .
When the one-foot cube is added, the water looks like this:
Code:
*-----------*
/ /|
/ / *
/ / /|
*-----------* / |
d| |/ |
* - - - - - * *
| | /
h| | /2
| |/
* - - - - - *
3
The water has risen to a height of feet.
This volume is:
. . which is 1 cubic foot more than the original volume.
So we have: .
. . . . . . .
Therefore, the water rises 2 inches.