Answer:
58 minutes
Step-by-step explanation:
You want the time it takes to fill a 10 ft hemisphere at the rate of 34 gallons per minute, using 1 ft³ = 7.5 gallons.
Volume
The volume of a hemisphere is given by ...
V = (1/2)(4/3)πr³ = 2/3πr³ . . . . . . where r = half the diameter
In cubic feet, the volume is ...
V = 2/3π(5 ft)³ = 250π/3 ft³ ≈ 261.799 ft³
In gallons, that will be ...
V = (261.799 ft³)×(7.5 gal/ft³) ≈ 1963.50 gal
Time
At the fill rate of 34 gallons/minute, the time required is ...
(1963.50 gal)/(34 gal/min) ≈ 57.75 min
It will take about 58 minutes to fill the tank completely.
