To determine if the new drinking water bottle can provide one cup of water for each of the 550 people, we'll compare the volume of the original bottle to the volume of the new bottle.

Step 1: Calculate the volume of the original bottle

The volume $V$ of a cylinder is given by the formula: $V = \pi r^2 h$ where:

• $r$ is the radius of the cylinder,
• $h$ is the height of the cylinder.

Let's denote:

• $r_1$ as the radius of the original bottle,
• $h$ as the height (same for both bottles).

So, the volume of the original bottle is: $V_1 = \pi r_1^2 h$

Step 2: Calculate the volume of the new bottle

For the new bottle, the radius is three times larger, so: $r_2 = 3r_1$ The volume of the new bottle is: $V_2 = \pi r_2^2 h = \pi (3r_1)^2 h = \pi \cdot 9r_1^2 \cdot h$ $V_2 = 9 \cdot \pi r_1^2 h = 9V_1$ This means the volume of the new bottle is 9 times the volume of the original bottle.

Step 3: Conclusion

Since the new bottle has 9 times the capacity of the original bottle, and the original bottle was insufficient, the new bottle should be more than sufficient to provide one cup of water for each of the 550 people.

Would you like more details or have any questions? Here are some related questions to consider:

1. How would the volume change if the radius doubled instead of tripled?
2. What if the height of the bottle was also doubled along with the radius?
3. How much water would each person receive if the radius was only doubled?
4. How does the volume of the cylinder change if only the height is increased?
5. How many cups of water could be provided if the new bottle's height doubled as well?

Tip: Always remember that the volume of a cylinder depends on both the square of the radius and the height. Changing the radius has a more significant impact on volume compared to changing the height.