Let's break this problem down and solve it step by step:

Part (i):

We are asked to find the time taken to pour 300 liters of water into the cylindrical container at a rate of 375 ml per second.

1. Convert 300 liters to milliliters (since the pouring rate is in ml/sec): $1 \, \text{liter} = 1000 \, \text{ml}$ So, $300 \, \text{liters} = 300 \times 1000 = 300,000 \, \text{ml}$

2. The rate of pouring water is 375 ml/second, so the time taken $t$ in seconds can be calculated by dividing the total volume by the rate: $t = \frac{300,000 \, \text{ml}}{375 \, \text{ml/s}} = 800 \, \text{seconds}$

3. Convert 800 seconds into minutes and seconds: $800 \, \text{seconds} = 13 \, \text{minutes} \, 20 \, \text{seconds}$

Thus, the time taken is 13 minutes 20 seconds.

Part (ii):

Next, we are asked to calculate the height of the water in the container once all the water is poured in. The formula for the volume $V$ of a cylinder is: $V = \pi r^2 h$ Where:

• $V$ is the volume of the water,
• $r$ is the radius of the base, which is 0.45 m,
• $h$ is the height of the water, which we need to find.

We know the total volume of water in the container is 300 liters (or 0.3 m³, since $1 \, \text{m}^3 = 1000 \, \text{liters}$).

1. Rearrange the volume formula to solve for the height $h$: $h = \frac{V}{\pi r^2}$
2. Substitute the known values ($V = 0.3 \, \text{m}^3$, $r = 0.45 \, \text{m}$): $h = \frac{0.3}{\pi (0.45)^2}$ $h = \frac{0.3}{\pi \times 0.2025}$ $h \approx \frac{0.3}{0.6362}$ $h \approx 0.4716 \, \text{m}$

Thus, the height of the water in the container is approximately 0.472 meters.

Do you want more details or have any questions about the solution?

Here are 5 related questions to expand your understanding:

1. How would the time change if the rate of pouring were doubled to 750 ml/second?
2. What would be the height of the water if only 150 liters were poured instead of 300 liters?
3. How would the height change if the radius of the container were increased to 0.6 meters?
4. What is the total surface area of the water's surface when it's fully poured into the container?
5. How can the formula for the volume of a cylinder be derived from the concept of a circle?

Tip: Always ensure units are consistent when solving real-world problems. In this case, we converted liters to milliliters and meters when necessary.