Answer:
approximately 3 days
Step-by-step explanation:
Given:
- population = 45000
- litres per person per day = 12
- radius = 7 meters
- height = 20 meters
Volume of the cylindrical reservoir when full
[tex]volume_{full} = \pi \times (radius^2) \times height[/tex]
[tex]volume_{full} = \pi \times (7m^2) \times 20m[/tex]
[tex]volume_{full} = \pi \times (49m^2) \times 20m[/tex]
[tex]volume_{full} =980 \pi m^3[/tex]
Convert cubic meters to litres (1 cubic meter = 1000 litres)
volume full litres = [tex]980\pi m^3 \times 1000[/tex]
= [tex]980000\pi \text{ liters}[/tex]
Half-filled volume
volume half litres = [tex]\frac{980000\pi \text{ liters}}{2}[/tex]
= [tex]490000\pi \text{ liters}[/tex]
Daily water consumption of the community
daily consumption = [tex]population\times \text{litres per person per day}[/tex]
= 540,000 liters
Number of days the water will last
[tex]days =\frac{ \text{volume half litres}}{ \text{daily consumption}}[/tex]
[tex]days =\frac{ 490000 \pi }{ 540000}[/tex]
[tex]days \approx 0.9074 \pi \implies 2.85 \: \: days[/tex]
Round to the nearest day
2.85 being above 5 in the decimal digits, we will add 1 to it, making it 3.
Therefore, the reservoir will last for approximately 3 days
