Final answer:
a. The rate at which the tank is filled is 16.5 gallons per second. b. The rate at which the tank is filled is 0.0273 cubic meters per second. c. It would take approximately 36.6 seconds to fill a 1.00 m³ volume at the same rate.
Step-by-step explanation:
a. To calculate the rate at which the tank is filled in gallons per second, we need to convert the time from minutes to seconds and divide the volume of the tank by the time taken to fill it.
1 gallon = 231 cubic inches
30 gallons = 30 x 231 cubic inches = 6930 cubic inches
Rate = Volume / Time
= 6930 cubic inches / (7 minutes x 60 seconds/minute)
= 16.5 cubic inches/second
b. To calculate the rate at which the tank is filled in cubic meters per second, we need to convert the volume from gallons to cubic meters and divide it by the time taken to fill the tank.
1 cubic meter = 1000 liters
1 gallon = 3.785 liters
30 gallons = 30 x 3.785 liters = 113.55 liters
1 liter = 0.001 cubic meters
113.55 liters = 113.55 x 0.001 cubic meters = 0.11355 cubic meters
Rate = Volume / Time
= 0.11355 cubic meters / (7 minutes x 60 seconds/minute)
= 0.0273 cubic meters/second
c. To determine the time interval required to fill a 1.00-m³ volume at the same rate, we need to divide the volume by the rate.
Time = Volume / Rate
= 1.00 m³ / 0.0273 cubic meters/second
= 36.6 seconds