Capacity is the quantity of liquid (or other pourable substance) that an item can organize when the full. When a liquid, such as milk, is being described in gallons or quarts, this is a measure up of capacity.

Understanding systems of capacity can assist you solve troubles like this: Sven and Johanna to be hosting a potluck dinner. Lock did not ask your guests to tell lock what they would be bringing, and also three people ended increase bringing soup. Erin lugged 1 quart, Richard carried 3 pints, and LeVar carried 9 cups. How many cups of soup did they have actually all together?


Units the Capacity


There are 5 main systems for measuring capacity in the U.S. Customary measurement system. The the smallest unit of measure up is a A unit of volume equal to

*
 of a cup. One liquid ounce that water in ~ 62°F weighs around one ounce.

You are watching: Explain one relationship between capacity and fluid ounces


")">fluid ounce
. “Ounce” is also used as a measure up of weight, so it is vital to use the word “fluid” with ounce once you are talking about capacity. Occasionally the prefix “fluid” is not supplied when that is clean from the context the the measure is capacity, not weight.

The various other units of capacity in the customary mechanism are the cup, pint, quart, and gallon. The table listed below describes every unit of capacity and also provides an instance to highlight the dimension of the unit of measurement.


Fluid Ounce

A unit of capacity equal come

*
 of a cup. One fluid ounce of water in ~ 62°F weighs around one ounce. The amount of liquid medicine is often measured in liquid ounces.

*

Cup

A unit same to 8 fluid ounces. The capacity of a conventional measuring cup is one cup.

*

Pint

A unit equal to 16 liquid ounces, or 2 cups. The capacity of a carton of ice cream cream is regularly measured in pints.

*

Quart

A unit equal to 32 liquid ounces, or 4 cups. You frequently see quarts the milk being sold in the supermarket.

*

Gallon

A unit equal to 4 quarts, or 128 liquid ounces. Once you to fill up your vehicle with gasoline, the price that gas is often provided in dollars per gallon.

*
 


You have the right to use any of these five measurement systems to describe the capacity of one object, yet it makes much more sense come use specific units for particular purposes. For example, that makes more sense to explain the volume of a swimming pool in gallons and the volume of an high-quality perfume in liquid ounces.

Sometimes friend will have to convert in between units of measurement. For example, you could want to express 5 gallons the lemonade in cups if you room trying to determine how countless 8-fluid ounce servings the quantity of lemonade would yield.

The table below shows some of the most usual equivalents and also conversion components for the 5 customary devices of measure of capacity.


Unit Equivalents

Conversion determinants (heavier come lighter systems of measurement)

Conversion Factors

(lighter come heavier devices of measurement)

1 cup = 8 fluid ounces

*

*

1 pint = 2 cups

*

*

1 quart = 2 pints

*

*

1 quart = 4 cups

*

*

1 gallon = 4 quarts

*

*

1 gallon = 16 cups

*

*


Converting in between Units of Capacity


As with converting devices of length and weight, you can use the variable label method to convert from one unit of volume to another. An example of this an approach is shown below.


Example

Problem

How many pints is

*
 gallons?

*

Begin through reasoning around your answer. Due to the fact that a gallon is larger than a pint, expect the answer in pints to it is in a number greater than

*
.

*

*

*

The table above does not contain a conversion aspect for gallons and pints, so girlfriend cannot convert it in one step. However, you deserve to use quarts as an intermediate unit, as presented here.

Set increase the equation therefore that two sets of labels cancel—gallons and quarts.

*

*

Multiply and also simplify.

Answer

*
 gallons is 22 pints.


Example

Problem

How numerous gallons is 32 liquid ounces?

32 fluid ounces = ___ gallons

Begin through reasoning about your answer. Because gallons is a bigger unit than fluid ounces, expect the answer to be much less than 32.

*

The table over does not contain a conversion factor for gallons and also fluid ounces, so girlfriend cannot transform it in one step. Use a series of intermediary units, as shown here.

*

*

Cancel systems that show up in both the numerator and denominator.

*

*

Multiply and also simplify.

Answer

32 liquid ounces is the same as

*
 gallon.


Find the sum of 4 gallons and 2 pints. Express her answer in cups.

A) 68 cups

B) 6 cups

C) 2 gallons and 4 pints

D) 34 pints


Show/Hide Answer

A) 68 cups

Correct. Every gallon has 16 cups, therefore 4 · 16 = 64 will provide you the variety of cups in 4 gallons. Every pint has actually 2 cups, for this reason 2 · 2 = 4 will provide you the variety of cups in 2 pints. 64 + 4 = 68 cups.

B) 6 cups

Incorrect. Friend cannot include measurements expressed in different units. First convert every amount come cups and then add. The exactly answer is 68 cups.

C) 2 gallons and 4 pints

Incorrect. This is not the exactly amount. First convert every amount to cups and then include them together. Also, notice that this answer is not expressed in cups, together the trouble requires. The correct answer is 68 cups.

D) 34 pints

Incorrect. This is the exactly amount, however it is to express in the untrue unit—pints. Main point 34 pints by 2 (since there space 2 cup in a pint) to provide the lot in cups as required. The correct answer is 68 cups.

Applying Unit Conversions


There are times once you will require to incorporate measurements the are given in various units. In stimulate to execute this, you have to convert very first so that the units are the same.

Consider the situation posed earlier in this topic.


Example

Problem

Sven and Johanna were hosting a potluck dinner. They did no ask your guests come tell castle what they would be bringing, and three people ended increase bringing soup. Erin carried 1 quart, Richard lugged 3 pints, and LeVar carried 9 cups. Exactly how much soup walk they have total?

1 quart + 3 pints + 9 cups

Since the problem asks because that the complete amount the soup, you must include the 3 quantities. Prior to adding, girlfriend must transform the amounts to the very same unit.

The problem does not call for a particular unit, so you can choose. Cups can be the simplest computation.

1 quart = 4 cups

This is given in the table that equivalents.

*

*

Use the factor label technique to convert pints come cups.

4 cups + 6 cup + 9 cup =

19 cups

Add the 3 quantities.

Answer

There space 19 cups of soup because that the dinner.


Example

Problem

Natasha is do lemonade to carry to the beach. She has two containers. One hold one gallon and the other holds 2 quarts. If she filling both containers, how many cups that lemonade will she have?

1 gallon + 2 quarts = ___ cups

This trouble requires girlfriend to uncover the amount of the volume of every container and also then transform that sum to cups.

4 quarts + 2 quarts = 6 quarts

First, discover the amount in quarts. 1 gallon is equal to 4 quarts.

*
 = ___ cups

*
 = ___ cups

6 • 2 • 2 = 24 cups

Since the problem asks because that the capacity in cups, transform 6 quarts to cups.

Cancel systems that show up in both the numerator and denominator.

Multiply.

Answer

Natasha will have 24 cup of lemonade.


Another means to work the problem over would be to first change 1 gallon come 16 cup and change 2 quarts come 8 cups. Climate add: 16 + 8 = 24 cups.

Alan is make chili. That is utilizing a cooking recipes that provides 24 cup of chili. He has a 5-quart pot and also a 2-gallon pot and is make the efforts to determine whether the chili will certainly all fit in among these pots. Which of the pots will fit the chili?

A) The chili will certainly not fit into either that the pots.

B) The chili can fit into either pot.

C) The chili will certainly fit into the 5-quart pot only.

D) The chili will certainly fit right into the 2-gallon pot only.


Show/Hide Answer

A) The chili will not fit into either the the pots.

Incorrect. The 5-quart pot will hold only 20 cups, leaving 4 cup that won’t fit right into the pot. However, the 2-gallon pot is huge enough to fit the chili. The exactly answer is the 2-gallon pot only.

B) The chili can fit right into either pot.

Incorrect. The 5-quart pot will hold only 20 cups, so the 24 cups of chili cannot fit in there. The correct answer is the 2-gallon pot only.

C) The chili will fit right into the 5-quart pot only.

Incorrect. The 5-quart pot will organize only 20 cups. The 2-gallon pot will organize 32 cups. The exactly answer is the 2-gallon pot only.

D) The chili will certainly fit right into the 2-gallon pot only.

Correct. 5 quarts = 5 • 4 cup = 20 cups, for this reason 24 cup of chili will not fit right into the 5-quart pot. 2 gallons = 32 cups, for this reason 24 cups of chili will certainly fit in this pot.

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Summary


There are five simple units for measuring capacity in the U.S. Customary measure up system. These room the fluid ounce, cup, pint, quart, and gallon. This measurement devices are pertained to one another, and capacity have the right to be described using any type of of the units. Typically, world use gallons to describe larger quantities and fluid ounces, cups, pints, or quarts to describe smaller quantities. Often, in stimulate to to compare or come solve troubles involving the lot of liquid in a container, you need to convert from one unit that measurement come another.