Final answer:
The total mass of the water and the Eureka can before the metal was lowered is 200g, calculated by assuming the can is filled to capacity and using the given density of water as 1g/cm³.
Step-by-step explanation:
To calculate the total mass of water and the Eureka can before the metal was lowered, we must first identify the initial conditions. Given that the Eureka can has a mass of 100g and a cross-sectional area of 100cm2, we can assume it is initially filled with water right up to the top. Since the density of water is 1g/cm3, the volume of water inside the can would be exactly equal to its cross-sectional area multiplied by its height. However, the question doesn't provide the height of water, so we can logically assume the volume of the Eureka can is filled to capacity.
The mass of water would therefore be equal to the volume of the can multiplied by the density of water. If the Eureka can's cross-sectional area represents its base area and the can is filled to the top, the entire volume of the can is filled with water. To get the volume in cubic centimeters, you would typically multiply base area by height, but since we do not have the height and the water's density directly equates its mass in grams for our volume in cubic centimeters (given by the density 1g/cm3), the mass of water equals the area in this case due to the given density. So the mass of water is 100g, matching the cross-sectional area. The total mass before the metal piece is added is the mass of the empty can plus the mass of the water, giving us 200g.