"Published in Newark, California, USA"
An ink bottle is in the form of a right circular cylinder with a large conical opening as shown in the figure. When it is filled with the bottom of the opening, it can just be turned upside down without any ink spilling. Prove that the depth of the cone is 3/5 the depth of the bottle.
 |
| Photo by Math Principles in Everyday Life |
Solution:
When you flipped the ink bottle, there should be no spills of ink as shown below
 |
| Photo by Math Principles in Everyday Life |
The vertical section of the above figure will be like this
 |
| Photo by Math Principles in Everyday Life |
As you can see in the figure that the level of the ink is exactly at the tip of the right circular cone. If it is above the tip of the right circular cone, then there will be the spillage of the ink. Let's label further the given figure as shown below
 |
| Photo by Math Principles in Everyday Life |
Volume before Inversion = Volume after Inversion
but
The above equation becomes
Therefore
