Lesson 78: Capacity

New Concept

Containers are named by their capacity, that is, by the amount of liquid they can contain.

What’s next

Next, you’ll use standard units like gallons and liters to compare container sizes and solve conversion problems.

Property

U.S. Customary System units are related as follows: 1 gallon = 4 quarts, 1 quart = 2 pints, 1 pint = 2 cups, and 1 cup = 8 ounces. Notice a pattern? Besides cups to ounces, each larger unit is double the next smaller unit, making a quart one 'quarter' of a gallon.

• A half gallon of milk is how many pints? $1 \text{ half-gallon} = 2 \text{ quarts} = 2 \times (2 \text{ pints}) = 4 \text{ pints}$. * How many cups are in a quart? $1 \text{ quart} = 2 \text{ pints} = 2 \times (2 \text{ cups}) = 4 \text{ cups}$. * A gallon of ice cream is how many cups? $1 \text{ gallon} = 4 \text{ quarts} = 16 \text{ cups}$.

Think of it like a liquid family tree! A big gallon has four quart-kids. Each quart has two pint-twins, and each pint has two cup-twins. This system is all about doubling down (mostly!), making it easier to remember how to pour the perfect amount for any recipe or drink, from a huge party punch to a single cup.

Property

In the metric system, liquid capacity is measured in liters (L) and milliliters (mL). The conversion is simple and based on the power of 1000:

• A 2-liter bottle has a capacity of how many milliliters? $2 \text{ L} = 2 \times 1000 \text{ mL} = 2000 \text{ mL}$. * Convert 500 milliliters to liters: $500 \text{ mL} = 500 \div 1000 \text{ L} = 0.5 \text{ L}$. * A science experiment requires 1.5 liters of water. How many milliliters is that? $1.5 \text{ L} = 1.5 \times 1000 \text{ mL} = 1500 \text{ mL}$.

The metric system loves the number 1000, and 'milli' is your clue—it means one-thousandth! So, a milliliter is just a tiny fraction of a liter. Imagine a big 2-liter soda bottle, which holds a whopping 2000 milliliters of fizzy fun. This simple relationship makes converting between units super quick and easy to remember.

Property

When comparing the two systems, the most important relationship to remember is that 1 liter is slightly more than 1 quart. This means that common containers like a 2-liter bottle and a half-gallon carton, while seemingly similar in size, do not hold the same amount of liquid. The 2-liter bottle has a little extra room.

• Which is greater, a 2-liter bottle or a half-gallon carton? Since $1 \text{ liter} > 1 \text{ quart}$, then $2 \text{ liters} > 2 \text{ quarts} (\text{a half-gallon})$. The 2-liter bottle is greater. * Which has more capacity, a 1-pint container or a 12-ounce can? A pint equals 16 ounces, so the 1-pint container has more capacity.

Ever get confused at the store? Just remember that a liter is a quart's slightly bigger cousin. This means a 2-liter soda bottle holds more than a half-gallon of milk, which is equal to 2 quarts. This simple trick helps you visualize and compare volumes without needing to do any complex calculations on the spot.