To find the maximum volume of water that can be filled in the bottle, we need to calculate the volume of the cylinder using the given formula:

$\text{Volume of a cylinder} = \pi r^2 h$

where:

• $\pi = \frac{22}{7}$
• $r$ is the radius of the cylinder
• $h$ is the height of the cylinder

From the image:

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

Let's calculate the volume.The maximum volume of water that can be filled in the bottle is approximately 14,142.86 cm³.

The correct answer is A. 14,142.86 cm³.

Would you like a detailed breakdown of this calculation or have any further questions?

Related Questions:

1. What would be the volume if the diameter was doubled?
2. How would the volume change if the height was increased to 60 cm?
3. How does the choice of π value (3.14 vs. 22/7) affect the volume calculation?
4. What is the surface area of this cylindrical bottle?
5. How do you calculate the volume of a cone?

Tip:

Remember that the volume formula for a cylinder relies heavily on the square of the radius; small changes in the radius result in larger changes in the volume.