There is some water in the bottle. We assume that sleep does not reach the bottleneck, and the radius of the bottle is equal except for the bottleneck.

Let the volume of water in the bottle be v and the volume of spare parts in the bottle be V 1.

There are:

V

+

V 1

=

1L (total volume in the bottle)

Let the inner radius of the bottle body part be r and the inner bottom radius of the cylindrical cup be r.

There are:

V

/

Pi*R*R

=

2 (When the bottle is placed upright, the water level is lower than 2 decimeters)

V 1

/

Pi*R*R

=

0.5 (when placed upside down, the height of spare parts is less than 0.5 decimeter)

The volume v of water can be solved by the above three equations:

V

=

0.8 liter

Then look inside the cylindrical glass:

V

/

Pi*r*r

=

1 (the water level in the cylindrical cup is 1 decimeter high)

According to this equation, the inner bottom area r of cylindrical water cup can be obtained:

r

=

5.05 cm

(Note: 1. In the expression here, it is difficult to find the symbol of hesitation Pi, and it is also difficult to find a single toilet, so it is directly replaced by pi;

2. unit of volume 1 liter is equal to 1 cubic decimeter, so it is more convenient for me to convert the length unit into decimeter. )