Question

One cubic centimeter of water has a mass of 1 gram. A milliliter is equal to a cubic centimeter. What is the mass, in kilograms, of a liter of water? A metric ton is a thousand kilograms. How many cubic centimeters of water are in a metric ton of water? If a metric ton of water were held in a thin-walled cubical tank, how long (in meters) would each side of the tank be?

Short answer

Answer: The mass of a liter of water is 1 kilogram. There are 1,000,000 cubic centimeters in a metric ton of water. Each side of the thin-walled cubical tank is 1 meter long.

Step-by-step solution

Convert the mass of a liter of water to kilograms

We know that 1 cubic centimeter (cc) of water has a mass of 1 gram, and there are 1000 cubic centimeters (cc) in a liter (L). Therefore, the mass of a liter of water is 1000 grams. Next, we need to convert 1000 grams to kilograms. There are 1000 grams in 1 kilogram, so the mass of a liter of water is 1 kilogram (kg).

Calculate the number of cubic centimeters of water in a metric ton of water

We know that 1 cubic centimeter of water has a mass of 1 gram. A metric ton is equal to 1000 kilograms, so it contains 1000 * 1000 = 1000000 grams. Since there is 1 gram of water per cubic centimeter, there must be 1000000 cubic centimeters of water in a metric ton of water.

Calculate the length of each side of a thin-walled cubical tank holding a metric ton of water

We need to find the side length of a cube with a volume of 1000000 cubic centimeters. To do this, we will use the formula for the volume of a cube: V = a^3, where V is the volume and a is the side length. We will solve for a by taking the cube root of the volume: a = V^(1/3) = 1000000^(1/3) Using a calculator, we find that a ≈ 100 centimeters. Since we want the side length in meters, we will convert 100 centimeters to meters: 100 cm * (1 m / 100 cm) = 1 meter Each side of the thin-walled cubical tank is 1 meter long.

Key concepts

Mass-Volume Relationship

The mass-volume relationship is a foundational concept in chemistry and physics that relates the mass of a substance to its volume. This relationship is particularly straightforward for water at 4°C (39.2°F), where 1 cubic centimeter (cc) of water has a mass of 1 gram (g). Therefore, in the context of water, the mass in grams and the volume in cubic centimeters are numerically equivalent.

Understanding this relationship is crucial when solving problems involving the calculation of mass from a given volume or vice versa. To determine the mass of a certain volume of water, you simply need to multiply the volume in cubic centimeters by 1 gram per cubic centimeter. This is because the density of water is essentially 1 g/cc, showing a direct mass-volume relationship.

Unit Conversion

Unit conversion is the process of converting the value of a physical quantity from one unit to another while maintaining the same measurement. In our exercise, we had to convert mass in grams to kilograms and volume in cubic centimeters to liters.

Unit conversion involves a basic understanding of the conversion factors between units. For example, since 1 kilogram is equivalent to 1000 grams, and 1 liter is equivalent to 1000 cubic centimeters, these conversion factors are used to switch between the units. Correct unit conversion is vital to ensure that mathematical calculations yield accurate results applicable in real-world scenarios.

Metric Ton Measurement

A metric ton is a unit of mass used in the metric system, commonly used across the world, except in the United States, where the short ton is often used. One metric ton is equal to 1000 kilograms or approximately 2204.62 pounds.

When working with large quantities of a substance, such as water in industrial or environmental contexts, the metric ton is often the preferred unit of measurement because it easily relates to kilogram, the base unit of mass in the International System of Units (SI). Understanding how to use metric tons in calculations is essential for tasks ranging from shipping to climate science, where large masses must be measured, conveyed, and understood.

Cubic Centimeters to Liters

Cubic centimeters and liters are two units of volume measurement. The conversion between these units is another common exercise in scientific calculations. There are 1000 cubic centimeters in 1 liter, making the conversion straightforward: to convert cubic centimeters to liters, you divide the number of cubic centimeters by 1000.

This conversion is crucial when dealing with volumes in different scales because cubic centimeters are more suitable for small, precise volumes, while liters are more convenient for larger volumes. Mastering the skill of converting cubic centimeters to liters is essential not only for solving textbook exercises but also for practical applications in laboratory and fieldwork.