Final answer:
The minimum volume of hot air required to lift a hot air balloon weighing 375 kg and carrying 3 persons weighing at least 68 kg each is calculated at 2316 cubic meters. The closest available choice given to 2316 cubic meters is 2500 cubic meters, which is sufficient for lift, therefore option (c) 2500 cubic meters is correct.
Step-by-step explanation:
The student is interested in understanding the principles of buoyancy related to hot air balloons and how the volume of hot air needed for lift is calculated according to the weight the balloon needs to carry. To calculate the minimum volume of hot air needed to lift the balloon and three people, we start with the understanding that one cubic meter of hot air can lift about 0.25 kg. By adding the weight of the balloon (375 kg) to the combined minimum weight of the three people (3 × 68 kg = 204 kg), we find the total weight that needs to be lifted is 579 kg.
To find the volume of hot air required to lift 579 kg, we divide the total weight by the weight that one cubic meter can lift:
Total weight to be lifted = 579 kg
Lift per cubic meter = 0.25 kg/m³
Volume required = 579 kg / 0.25 kg/m³ = 2316 m³
We can see that the minimum volume required is 2316 cubic meters. Since this option is not available among the choices, the next highest volume we can choose that will achieve buoyancy is 2500 cubic meters, making option (c) the correct choice.