https://file.aiquickdraw.com/mathbot/file/1725641362379fzhmia57.jpg

To calculate the volume of the cylindrical water dispenser, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

Where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder, and
- \( \pi \) is approximately \( \frac{22}{7} \) as given in the problem.

From the image:
- The diameter of the base is given as 42 cm, so the radius \( r \) is half of that: \( r = \frac{42}{2} = 21 \) cm.
- The height \( h \) is given as 40 cm.

Now, substitute these values into the volume formula:

\[
V = \frac{22}{7} \times (21)^2 \times 40
\]

Let's compute the volume.

\[
V = \frac{22}{7} \times 441 \times 40
\]

\[
V = \frac{22 \times 441 \times 40}{7}
\]

\[
V = \frac{387,120}{7}
\]

\[
V = 55,302.86 \text{ cubic centimeters}
\]

So, the volume of the water dispenser is approximately **55,303 cubic centimeters**.

Would you like more details on this solution or have any further questions?

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Here are five related questions you might find interesting:
1. How would the volume change if the height of the dispenser was increased by 10 cm?
2. What would be the volume if the radius was reduced by half?
3. How does changing the value of \( \pi \) (e.g., using \( \pi = 3.14 \)) affect the calculated volume?
4. How much water (in liters) can the dispenser hold?
5. What is the surface area of the cylindrical dispenser?

**Tip:** Remember, when working with cylinders, the radius plays a crucial role because the area of the base is \( \pi r^2 \), and any change in radius affects the volume significantly.

What is the volume of the water dispenser? (Use π = 22/7, Formula for the volume of a cylinder = πr^2h)

Learn how to calculate the volume of a closed cylindrical water dispenser with a diameter of 42 cm and a height of 40 cm. Using the formula V = πr^2h, this problem demonstrates key geometry concepts for middle school students.

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