In a certain community with a population of 45,000, it is estimated that each person needs 12 litres of water each day. The community has a centralized reservoir which is cylindrical with a radius of 7m and height 20m. If the reservoir is half filled, how long, to the nearest day, will the water last.​



Answer :

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