Answer :
### Step-by-Step Solution:
#### 1.1.1 Calculate the volume of the reservoir tank in [tex]\( m^3 \)[/tex]
We start by using the formula for the volume of a cylinder, which is given by:
[tex]\[ V = \pi r^2 h \][/tex]
Here,
[tex]\( \pi \approx 3.14 \)[/tex] (rounded to two decimal places),
- The diameter of the tank [tex]\(d = 18 \, \text{cm}\)[/tex]
- The height of the tank [tex]\(h = 30 \, \text{cm}\)[/tex]
First, we need to convert these dimensions to meters:
[tex]\[ d = 0.18 \, \text{m} \][/tex]
[tex]\[ h = 0.30 \, \text{m} \][/tex]
Next, we calculate the radius [tex]\(r\)[/tex] of the tank:
[tex]\[ r = \frac{d}{2} = \frac{0.18 \, \text{m}}{2} = 0.09 \, \text{m} \][/tex]
Now, we can calculate the volume using the formula:
[tex]\[ V = 3.14 \times (0.09 \, \text{m})^2 \times 0.30 \, \text{m} \][/tex]
[tex]\[ V = 3.14 \times 0.0081 \, \text{m}^2 \times 0.30 \, \text{m} \][/tex]
[tex]\[ V \approx 0.007630 \, \text{m}^3 \][/tex]
So, the volume of the reservoir tank is approximately [tex]\( 0.007630 \, \text{m}^3 \)[/tex].
#### 1.1.2 The reservoir can only be filled with [tex]\( 95 \% \)[/tex] of water. Calculate the amount of water inside the reservoir. Give your answer to the nearest [tex]\( m^3 \)[/tex]
To find the amount of water inside the reservoir when it is 95% filled, we multiply the total volume of the tank by 0.95:
[tex]\[ V_{\text{water}} = 0.95 \times 0.007630 \, \text{m}^3 \][/tex]
[tex]\[ V_{\text{water}} \approx 0.007249 \, \text{m}^3 \][/tex]
So, the amount of water inside the reservoir when filled to 95% is approximately [tex]\( 0.007249 \, \text{m}^3 \)[/tex].
#### 1.1.3 Determine the amount in [tex]\( kl \)[/tex] of water inside the reservoir. Round off your answer to the nearest [tex]\( kl \)[/tex]. Remember: [tex]\( 1 \, m^3 = 1000 \, l \)[/tex]
To convert the volume of water from cubic meters to kiloliters (kl), we need to use the conversion factor:
[tex]\[ 1 \, \text{m}^3 = 1 \, \text{kl} \][/tex]
So,
[tex]\[ V_{\text{water}} = 0.007249 \, \text{m}^3 \][/tex]
[tex]\[ V_{\text{water (kl)}} = 0.007249 \, \text{kl} \][/tex]
Since we need to round off to the nearest kiloliter:
[tex]\[ V_{\text{water (kl)}} \approx 0 \, \text{kl} \][/tex]
Hence, the amount of water inside the reservoir is approximately [tex]\( 0 \, \text{kl} \)[/tex].
#### 1.1.4 Calculate the amount in liters of water used by one person per day if a household of 5 members uses 2000 liters of water in a month of 30 days.
First, calculate the total water usage per day for the household:
[tex]\[ \text{Total daily usage} = \frac{\text{Total monthly usage}}{30 \, \text{days}} \][/tex]
[tex]\[ \text{Total daily usage} = \frac{2000 \, \text{liters}}{30 \, \text{days}} \][/tex]
[tex]\[ \text{Total daily usage} \approx 66.67 \, \text{liters/day} \][/tex]
Next, calculate the daily water usage per person:
[tex]\[ \text{Per person daily usage} = \frac{66.67 \, \text{liters/day}}{5 \, \text{people}} \][/tex]
[tex]\[ \text{Per person daily usage} \approx 13.33 \, \text{liters/day} \][/tex]
So, each person uses approximately [tex]\( 13.33 \, \text{liters} \)[/tex] of water per day.
#### 1.1.5 Mention two ways that can be used by the communities to access and preserve water.
1. Rainwater Harvesting: Communities can collect and store rainwater from rooftops or other surfaces to be used for various purposes, such as irrigation, domestic use, or replenishing groundwater.
2. Building Dams and Reservoirs: Constructing dams and reservoirs can help in managing water supply, storing excess water during the rainy season, and providing a controlled release of water during dry periods, ensuring a consistent water supply.
This detailed solution provides a thorough understanding of the problem and systematically arrives at the answer.
#### 1.1.1 Calculate the volume of the reservoir tank in [tex]\( m^3 \)[/tex]
We start by using the formula for the volume of a cylinder, which is given by:
[tex]\[ V = \pi r^2 h \][/tex]
Here,
[tex]\( \pi \approx 3.14 \)[/tex] (rounded to two decimal places),
- The diameter of the tank [tex]\(d = 18 \, \text{cm}\)[/tex]
- The height of the tank [tex]\(h = 30 \, \text{cm}\)[/tex]
First, we need to convert these dimensions to meters:
[tex]\[ d = 0.18 \, \text{m} \][/tex]
[tex]\[ h = 0.30 \, \text{m} \][/tex]
Next, we calculate the radius [tex]\(r\)[/tex] of the tank:
[tex]\[ r = \frac{d}{2} = \frac{0.18 \, \text{m}}{2} = 0.09 \, \text{m} \][/tex]
Now, we can calculate the volume using the formula:
[tex]\[ V = 3.14 \times (0.09 \, \text{m})^2 \times 0.30 \, \text{m} \][/tex]
[tex]\[ V = 3.14 \times 0.0081 \, \text{m}^2 \times 0.30 \, \text{m} \][/tex]
[tex]\[ V \approx 0.007630 \, \text{m}^3 \][/tex]
So, the volume of the reservoir tank is approximately [tex]\( 0.007630 \, \text{m}^3 \)[/tex].
#### 1.1.2 The reservoir can only be filled with [tex]\( 95 \% \)[/tex] of water. Calculate the amount of water inside the reservoir. Give your answer to the nearest [tex]\( m^3 \)[/tex]
To find the amount of water inside the reservoir when it is 95% filled, we multiply the total volume of the tank by 0.95:
[tex]\[ V_{\text{water}} = 0.95 \times 0.007630 \, \text{m}^3 \][/tex]
[tex]\[ V_{\text{water}} \approx 0.007249 \, \text{m}^3 \][/tex]
So, the amount of water inside the reservoir when filled to 95% is approximately [tex]\( 0.007249 \, \text{m}^3 \)[/tex].
#### 1.1.3 Determine the amount in [tex]\( kl \)[/tex] of water inside the reservoir. Round off your answer to the nearest [tex]\( kl \)[/tex]. Remember: [tex]\( 1 \, m^3 = 1000 \, l \)[/tex]
To convert the volume of water from cubic meters to kiloliters (kl), we need to use the conversion factor:
[tex]\[ 1 \, \text{m}^3 = 1 \, \text{kl} \][/tex]
So,
[tex]\[ V_{\text{water}} = 0.007249 \, \text{m}^3 \][/tex]
[tex]\[ V_{\text{water (kl)}} = 0.007249 \, \text{kl} \][/tex]
Since we need to round off to the nearest kiloliter:
[tex]\[ V_{\text{water (kl)}} \approx 0 \, \text{kl} \][/tex]
Hence, the amount of water inside the reservoir is approximately [tex]\( 0 \, \text{kl} \)[/tex].
#### 1.1.4 Calculate the amount in liters of water used by one person per day if a household of 5 members uses 2000 liters of water in a month of 30 days.
First, calculate the total water usage per day for the household:
[tex]\[ \text{Total daily usage} = \frac{\text{Total monthly usage}}{30 \, \text{days}} \][/tex]
[tex]\[ \text{Total daily usage} = \frac{2000 \, \text{liters}}{30 \, \text{days}} \][/tex]
[tex]\[ \text{Total daily usage} \approx 66.67 \, \text{liters/day} \][/tex]
Next, calculate the daily water usage per person:
[tex]\[ \text{Per person daily usage} = \frac{66.67 \, \text{liters/day}}{5 \, \text{people}} \][/tex]
[tex]\[ \text{Per person daily usage} \approx 13.33 \, \text{liters/day} \][/tex]
So, each person uses approximately [tex]\( 13.33 \, \text{liters} \)[/tex] of water per day.
#### 1.1.5 Mention two ways that can be used by the communities to access and preserve water.
1. Rainwater Harvesting: Communities can collect and store rainwater from rooftops or other surfaces to be used for various purposes, such as irrigation, domestic use, or replenishing groundwater.
2. Building Dams and Reservoirs: Constructing dams and reservoirs can help in managing water supply, storing excess water during the rainy season, and providing a controlled release of water during dry periods, ensuring a consistent water supply.
This detailed solution provides a thorough understanding of the problem and systematically arrives at the answer.
