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Answer :
To find the flow rate in liters per second, let's break down the problem step-by-step:
1. Volume of the Room:
The pipes can carry a volume of water equivalent to a room with dimensions 6 meters by 3 meters by 3 meters. To find the volume of this room, we calculate:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = 6 \, \text{m} \times 3 \, \text{m} \times 3 \, \text{m} = 54 \, \text{cubic meters}
\][/tex]
2. Convert Volume to Liters:
Since 1 cubic meter is equivalent to 1,000 liters, we convert the volume from cubic meters to liters:
[tex]\[
54 \, \text{cubic meters} \times 1000 \, \text{liters/cubic meter} = 54,000 \, \text{liters}
\][/tex]
3. Flow Rate in Liters per Minute:
The pipes carry 54,000 liters per minute, because this is the equivalent volume specified in the problem for each minute.
4. Convert to Liters per Second:
To find out how many liters per second the pipes carry, divide the liters per minute by 60 (since there are 60 seconds in a minute):
[tex]\[
\frac{54,000 \, \text{liters}}{60 \, \text{seconds}} = 900 \, \text{liters per second}
\][/tex]
So, the flow rate is 900 liters per second. The correct answer is 900 L/s.
1. Volume of the Room:
The pipes can carry a volume of water equivalent to a room with dimensions 6 meters by 3 meters by 3 meters. To find the volume of this room, we calculate:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = 6 \, \text{m} \times 3 \, \text{m} \times 3 \, \text{m} = 54 \, \text{cubic meters}
\][/tex]
2. Convert Volume to Liters:
Since 1 cubic meter is equivalent to 1,000 liters, we convert the volume from cubic meters to liters:
[tex]\[
54 \, \text{cubic meters} \times 1000 \, \text{liters/cubic meter} = 54,000 \, \text{liters}
\][/tex]
3. Flow Rate in Liters per Minute:
The pipes carry 54,000 liters per minute, because this is the equivalent volume specified in the problem for each minute.
4. Convert to Liters per Second:
To find out how many liters per second the pipes carry, divide the liters per minute by 60 (since there are 60 seconds in a minute):
[tex]\[
\frac{54,000 \, \text{liters}}{60 \, \text{seconds}} = 900 \, \text{liters per second}
\][/tex]
So, the flow rate is 900 liters per second. The correct answer is 900 L/s.
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