Final answer:
1 kg of gasoline takes up more space than 1 kg of water due to its lower density. For a tank holding 50 kg of gasoline measuring 0.5 m by 0.9 m, the depth would be approximately 14.8 cm. This size is reasonable for a passenger car's gasoline tank.
Step-by-step explanation:
To answer the question of whether 1 kg of water or 1 kg of gasoline takes up more space, we need to understand the concept of density, which is mass per unit volume (density = mass / volume). Given that water has a density of approximately 1 kg/L, this means that 1 kg of water occupies 1 liter of space. Gasoline, on the other hand, has a density of about 0.75 kg/L, meaning that 1 kg of gasoline would occupy approximately 1.33 liters (since volume = mass / density, which is 1 kg / 0.75 kg/L). Therefore, 1 kg of gasoline takes up more space than 1 kg of water. The correct answer is b) 1 kg of gasoline.
Regarding the gasoline tank question, to find the depth, we divide the mass of the gasoline by the product of its density and the area of the base of the tank. Given a mass of 50.0 kg and a density of 0.75 kg/L, we first convert mass to volume: volume = mass / density = 50.0 kg / 0.75 kg/L = 66.67 L. Since 1 L is equal to 1 cubic decimeter (dm³), the volume in cubic meters is 0.06667 m³. Finally, we divide the volume by the area of the base (0.500 m * 0.900 m): depth = volume / area = 0.06667 m³ / (0.500 m * 0.900 m) = approx 0.148 m, or 14.8 cm.
A reasonable volume for a passenger car's gasoline tank is about 50 L. Since the calculated volume of the tank is close to the typical volume for a passenger vehicle, we can conclude that this is a reasonable size for a passenger car's gas tank.