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?
It would take 2 hours for the hose to fill a cubical tank of edge length 2 meters.
The volume of a cubical tank increases with the cube of its edge length. Therefore, a tank with an edge length of 2 meters has a volume that is eight times larger than that of a 1-meter tank, requiring proportionally more time to fill.
This choice implies that the time to fill the larger tank is only 30 minutes, which is unrealistic given that the larger tank holds eight times the volume of the smaller tank. The filling rate is insufficient to achieve this, considering the hose takes 15 minutes to fill a 1-meter tank.
Choosing 1 hour suggests that the hose could fill the larger tank in 60 minutes. However, since the larger tank has eight times the volume, it would take eight times the time of the smaller tank, which translates to 120 minutes or 2 hours, making this choice incorrect.
This option indicates a filling time of 90 minutes, which still does not account for the increased volume of the larger tank. Since the hose fills the smaller tank in 15 minutes, filling the larger tank would logically require 120 minutes, rendering this choice incorrect.
This choice accurately reflects the time required to fill the larger tank. Given that the volume of the 2-meter tank is eight times that of the 1-meter tank, and the hose fills the smaller tank in 15 minutes, it will take 8 times 15 minutes, resulting in 120 minutes or 2 hours for the larger tank.
The filling time for a tank increases with the cube of its edge length due to the volume relationship. A 2-meter cubical tank has a volume eight times greater than a 1-meter tank, necessitating a fill time of 2 hours. Understanding this relationship is crucial for accurately calculating fill times based on tank dimensions.
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