2. A hose can fill a cubical tank of edge length 1 meter in 15 minutes. At this rate, how long would it take for the hose to fill a cubical tank of edge length 2 meters?
Answer: D
It would take 2 hours for the hose to fill a cubical tank of edge length 2 meters.
The volume of a cubical tank is calculated by cubing its edge length. A tank with an edge length of 2 meters has a volume of 8 cubic meters, which requires four times the time to fill compared to a 1-meter tank, resulting in a total filling time of 2 hours.
A) 1/2 hours
This option is incorrect because it suggests that the filling time is significantly shorter than the actual required time. Since the volume of the larger tank is four times greater than the smaller tank, it cannot be filled in just 30 minutes.
B) 1 hour
This option is also incorrect as it implies that the time required is only double that of the smaller tank. However, given the volume increase, it actually requires four times the time to fill, indicating that 1 hour is insufficient.
C) 1.5 hours
This option does not accurately reflect the necessary time to fill the larger tank. Although it is closer than the previous options, it still underestimates the time needed, which is confirmed to be 2 hours based on the volume calculations.
D) 2 hours
This is the correct option since the volume of the cubical tank with an edge length of 2 meters is 8 cubic meters. Given that the hose fills 1 cubic meter in 15 minutes, it would take 60 minutes, or 1 hour, for 4 cubic meters, thus taking a total of 2 hours to fill the entire tank.
Conclusion
The correct answer is 2 hours because the volume of the larger tank necessitates four times the filling time of the smaller tank. All other options fail to account for the significant increase in volume, leading to underestimations of the time required to fill the tank.