https://file.aiquickdraw.com/mathbot/file/1724213532512hiu40fbw.jpg

Mesin pembahagi air dipasang dengan botol air minuman berbentuk silinder seperti rajah berikut.

UNIT 7: ITEM 7a

*

Berapakah isi padu maksimum air boleh diisi dalam botol tersebut? (Gunakan 𝜋 = 22/7 , Rumus isi padu silinder = 𝜋𝑗2𝑡)

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!

Learn how to calculate the maximum volume of water that can be filled in a cylindrical water bottle using the formula for the volume of a cylinder. Given the dimensions of the cylinder (diameter 20 cm, height 45 cm) and π = 22/7, the calculated volume is approximately 14142.86 cm³.

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