The available drinking water is insufficient to provide one cup each for 550 people. 

The new drinking water bottle, with the same height but the radius is three times larger than the original, has been equipped. 

Is the capacity of the new drinking water bottle sufficient?   


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.

The available drinking water is insufficient to provide one cup each for 550 people. The new drinking water bottle, with the same height but the radius is three times larger than the original, has been equipped. Is the capacity of the new drinking water bottle sufficient?

Determine if a new water bottle with a tripled radius is sufficient to provide one cup of water each for 550 people. This problem involves calculating the volume of a cylinder and understanding how changes in radius affect the volume. Ideal for students in Grades 8-10.

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