https://file.aiquickdraw.com/mathbot/file/1726619681560d4vwhceb.jpg

Let's go through the problem step by step.

### Part (b) (i):
The rectangle represents the net of the curved surface of a cylinder. The dimensions of the rectangle are:
- \( a \) is the circumference of the base of the cylinder.
- \( b \) is the height of the cylinder.

The formula for the circumference of a circle is:
\[
a = 2\pi r
\]
where \( r \) is the radius of the base of the cylinder.

The height of the cylinder is directly given by \( b \), which is the same as the height of the rectangle.

Thus, to find \( a \) and \( b \), we need the radius \( r \) and height from earlier in the question (likely provided in part (a), which is not visible).

### Part (b) (ii):
The area of the curved surface of the cylinder is given by the area of the rectangle, which is:
\[
\text{Area} = a \times b = (2\pi r) \times h
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.

### Part (c):
Here, you are asked to calculate the height of water in the cylinder when 0.5 liters (or 500 cubic centimeters) of water is poured into it.

The volume of a cylinder is given by:
\[
V = \pi r^2 h
\]
We can rearrange this to solve for the height of the water (\( h \)) when the volume is given:
\[
h = \frac{V}{\pi r^2}
\]
You will need the radius \( r \) of the cylinder to complete this calculation.

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If you provide the radius or other relevant data from part (a), I can proceed with exact calculations.

Let me know if you'd like more details, or help with solving any specific part.

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Here are 5 related questions to explore:
1. How do you derive the formula for the area of a cylinder's curved surface?
2. Why is the volume formula for a cylinder based on the area of a circle?
3. How can you use the water level formula in other shapes, such as cones?
4. What happens to the surface area of a cylinder if the radius is doubled but the height remains the same?
5. How does the formula for the surface area of a sphere differ from that of a cylinder?

**Tip**: Always verify units when dealing with volumes (liters to cubic centimeters) to avoid errors in calculations.

The rectangle shown below, not drawn to scale, represents the net of the curved surface of the cylinder shown above. (i) State the values of a and b. (ii) Hence, calculate the area of the curved surface of the cylinder. If 0.5 litres of water is poured into the cylinder, calculate, correct to one decimal place, the height of water in the cylinder.

Learn how to calculate the curved surface area and volume of a cylinder. This problem uses formulas for the circumference, surface area, and volume to solve for the height of water and the area of the curved surface. Suitable for students in Grades 10-11.

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