https://file.aiquickdraw.com/mathbot/file/1724213717617nralcou6.jpg

Sebiji cawan berbentuk silinder disediakan seperti dalam rajah.  


Cawan itu diisi penuh dengan air minuman dan hanya akan digunakan sekali. 

Berapakah bilangan biji cawan yang perlu disediakan? 

Your answer

UNIT 7: ITEM 7c

*

Air minuman yang disediakan tidak mencukupi untuk seorang sebiji cawan bagi 550 orang. 

Saiz botol air minuman yang baharu dengan ketinggian yang sama tetapi jejari ialah tiga kali botol air minuman asal telah digantikan. 

Adakah saiz botol air minuman yang baharu mencukupi.
Tandakan (✓) pada ruang yang disediakan.

To solve the problem, we need to:

1. **Calculate the volume of one cup** (which is a cylinder).
2. **Calculate the volume of the original bottle** of water.
3. **Determine how many cups can be filled with the water in the original bottle.**
4. **Compare the volume of the new larger bottle** with the total volume needed for 550 cups.

### Step 1: Calculate the Volume of One Cup

The cup is cylindrical with:
- Diameter = 6 cm, so the radius \( r = \frac{6}{2} = 3 \) cm
- Height \( h = 9 \) cm

The formula for the volume of a cylinder is:

\[
V_{\text{cup}} = \pi r^2 h
\]

Substituting the values:

\[
V_{\text{cup}} = \frac{22}{7} \times 3^2 \times 9
\]

\[
V_{\text{cup}} = \frac{22}{7} \times 9 \times 9 = \frac{22}{7} \times 81 = \frac{1782}{7} \approx 254.57 \text{ cm}^3
\]

### Step 2: Calculate the Volume of the Original Bottle of Water

From the previous problem:
- The original bottle has a radius \( r = 10 \) cm and height \( h = 45 \) cm.

\[
V_{\text{bottle}} = \frac{22}{7} \times 10^2 \times 45 = 14142.86 \text{ cm}^3
\]

### Step 3: Determine the Number of Cups that Can be Filled

\[
\text{Number of cups} = \frac{V_{\text{bottle}}}{V_{\text{cup}}} = \frac{14142.86}{254.57} \approx 55.58
\]

Since you cannot have a fraction of a cup, you can only fill **55 full cups** with the water from the original bottle.

### Step 4: Compare with New Bottle

The new bottle has:
- The same height (\( h = 45 \) cm)
- Radius \( r \) that is three times the original: \( 3 \times 10 \) cm = 30 cm.

Calculate the volume of the new bottle:

\[
V_{\text{new bottle}} = \frac{22}{7} \times 30^2 \times 45
\]

\[
V_{\text{new bottle}} = \frac{22}{7} \times 900 \times 45 = \frac{22}{7} \times 40500 = \frac{891000}{7} \approx 127285.71 \text{ cm}^3
\]

### Determine if the New Bottle is Enough for 550 Cups

Calculate the total volume needed for 550 cups:

\[
V_{\text{total cups}} = 550 \times 254.57 \approx 140013.5 \text{ cm}^3
\]

Compare with the volume of the new bottle:

\[
V_{\text{new bottle}} = 127285.71 \text{ cm}^3 \quad \text{vs} \quad V_{\text{total cups}} = 140013.5 \text{ cm}^3
\]

Since **127285.71 cm³** is less than **140013.5 cm³**, the new bottle **is not enough** to fill 550 cups.

Would you like any further details or have any questions?

Here are some related questions:
1. What would happen if the new bottle’s radius was increased by 4 times instead of 3?
2. How much more water is needed to fill the 550 cups?
3. How many cups can the new bottle fill?
4. If the bottle’s height was doubled, how many cups could it fill then?
5. What is the minimum radius required to fill 550 cups with the current height?

**Tip:** When dealing with proportional changes in geometry, remember that volume changes with the cube of the scale factor when all dimensions are scaled, but with the square of the scale factor if only height or radius is scaled.

Learn how to calculate the volume of a cylindrical cup and determine if a larger bottle can hold enough water for 550 cups. This problem involves geometry and volume calculations, suitable for students in Grades 10-12.

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