To find the maximum volume of water that can be filled in the cylindrical water bottle, we can use the formula for the volume of a cylinder:

$V = \pi r^2 h$

where:

• $r$ is the radius of the cylinder (which is half the diameter),
• $h$ is the height of the cylinder,
• $\pi$ is given as $\frac{22}{7}$.

Given in the image:

• The diameter of the cylinder is 20 cm, so the radius $r$ is $\frac{20}{2} = 10$ cm.
• The height $h$ of the cylinder is 45 cm.

Now, we can calculate the volume $V$:

$V = \frac{22}{7} \times (10)^2 \times 45$

Let's compute this step by step:

1. $10^2 = 100$
2. $\frac{22}{7} \times 100 = \frac{2200}{7}$
3. $\frac{2200}{7} \times 45 = \frac{99000}{7}$

Finally, calculate $\frac{99000}{7}$:

$V \approx 14142.86 \, \text{cm}^3$

So, the maximum volume of water that can be filled in the bottle is approximately 14142.86 cm³.

Would you like any more details or have any questions?

Here are some related questions:

1. How would the volume change if the radius was doubled but the height remained the same?
2. What would happen to the volume if the height was reduced by half?
3. How does the value of $\pi$ (as $\frac{22}{7}$ versus $3.14$) affect the calculation?
4. How would you calculate the surface area of this cylinder?
5. If the cylinder was only half full, what would the volume of water be?

Tip: Remember that when solving geometry problems, always double-check units and ensure consistency throughout your calculations!