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.

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.

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.