Final answer:
The volume of the air mattress is calculated to determine its buoyancy in freshwater. It can displace 300 kg of water, which means the maximum weight it can support is 298 kg, after considering the weight of the mattress itself. However, this correct answer does not match any of the provided options.
Step-by-step explanation:
A student is curious to know how heavy a person could the twin-sized air mattress hold if it is placed in freshwater. The dimensions of the air mattress are 100 cm by 200 cm by 15 cm, and it weighs 2 kg.
To solve this, we would calculate the volume of the air mattress and then use the density of freshwater to determine the buoyancy force.
The volume V of the air mattress is V = length × width × height, which equals V = 100 cm × 200 cm × 15 cm = 300,000 cm³. Since 1 cm³ of freshwater has a mass of 1 gram, the air mattress can displace 300,000 grams (or 300 kg) of water when fully submerged.
The maximum weight the mattress can support is the weight it displaces minus its own weight. Therefore, the mattress can support up to 300 kg - 2 kg = 298 kg. Since none of the given options (180 kg, 200 kg, 220 kg, 240 kg) match this result, it appears there might be a mistake with the provided options.