Answer:
Time taken to fill the pool = 7.81 hours
Step-by-step explanation:
We are given that it takes 19 seconds to fill 2 gallons. Therefore, we can use cross multiplication to know how long will it take to fill one gallon as follows :
Time taken to fill 2 gallons of tank = 19 seconds
[tex]\text{Time taken to fill 1 gallons of tank = }\frac{19}{2}\text{ = 9.5 seconds}[/tex]
Therefore, it takes 9.5 seconds to fill one gallon of water.
One gallon is equivalent to 0.133681 cubic feet
Therefore, it takes 9.5 seconds to fill 0.133681 cubic feet
Now, to find Volume of the pool :
radius of pool = 6 ft
volume of pool = pi × (radius)² × height
volume of pool = 3.14 × 6² × 3.5
volume of pool = 395.64 cubic feet
Time taken to fill 0.133681 cubic feet of water = 9.5 sec
[tex]\text{Time taken to fill 395.34 cubic feet of water = }\frac{9.5}{0.133681}\times 395.64\\\\\implies\bf\textbf{Time taken to fill the pool = 28116.04 seconds}=\frac{28116.04}{60\times 60}\text{ hours}\\\approx 7.81\textbf{ hours}[/tex]
Hence, Time taken to fill the pool = 7.81 hours
