1 cm³ of water is equal to 1 ml of water, which is equal to 1 g of water. What is the mass of 1 m³ of water?
The Correct Answer and Explanation is:
To find the mass of 1 cubic meter (m³) of water, we need to use the given relationships:
- 1 cm³ of water = 1 mL of water
- 1 mL of water = 1 gram of water
These relationships tell us that the density of water is 1 g/cm³. Since the density is the mass per unit volume, it means that every 1 cm³ of water has a mass of 1 gram.
Now, let’s convert cubic meters to cubic centimeters:
1 meter = 100 centimeters
Therefore,
1 m³ = (100 cm) × (100 cm) × (100 cm) = 1,000,000 cm³
So, 1 cubic meter of water is 1,000,000 cm³ of water.
Since each cm³ of water has a mass of 1 gram, the total mass of 1 m³ of water would be:
1 m³ × 1,000,000 g = 1,000,000 grams
To express this in kilograms, since 1 kilogram = 1000 grams:
1,000,000 grams ÷ 1000 = 1000 kilograms
Thus, the mass of 1 m³ of water is 1000 kilograms.
Explanation:
Water has a density of approximately 1 gram per cubic centimeter (g/cm³) at standard temperature and pressure (STP). This is a useful value because it means that the mass of water in grams is numerically equal to its volume in cubic centimeters. By converting between units of volume (cubic meters to cubic centimeters) and applying the density, we can calculate that 1 m³ of water weighs 1000 kilograms. This is important for various applications in science, engineering, and everyday life, as it helps in calculating water storage, transport, and consumption.
