5th Grade Math
Volume and Measurement
Unit 6
Volume and Measurement
Converting Units of Measure
You have learned that there are units of measure for mass, weight, length, and time. In the U.S., we use the customary system while the rest of the world uses the metric system. Take a look at the chart below to see which units belong in the customary system and which units belong in the metric system. The chart also shows the abbreviation for each unit.
Sometimes we need to convert between units of measure so let's learn how to do it!
Metric units are very nice to work with, since they are all multiples of ten (or a hundred, or one-tenth, etc) of each other. You can convert between the various different sizes by merely moving the decimal point the correct number of places.
The basic metric units are meters (for length), grams (for mass or weight), and liters (for volume).
There are many metric-unit prefixes, but the usual ones are these: kilo-, hecto-, deka-, deci-, centi-, and milli- (as the chart shows above!).
To convert from one unit to another in the metric system, we just divide the given number by 10 if we are converting from a smaller unit to a bigger unit. This is the same thing as moving a decimal to the left.
Example:
Let's convert 200 grams to kilograms. In the chart, we see that Kilo is 3 spaces in front of the Unit measure (gram is a unit measurement), and since we are converting from a smaller unit to a bigger unit (going to the left on the chart), we need to divide 200 by 10 for each space. Therefore, we need to divide 200 by 10 three times! Dividing by 10 three times is the same as dividing by 1000 (10 x 10 x 10 = 1000). 200 divided by 1000 is 0.2. Our answer is 0.2 kilogram. You can see that we moved the decimal point to the left THREE times to get our answer since kilo is THREE spaces in front of our unit measurement.
An easy way to remember the order is ' King Henry Died Unusually Drinking Chocolate Milk', like you see in the chart above.
For customary units, we have to memorize the conversions since there is no rule like the metric system!
Try these games for more conversion practice!
Watch this video to learn how to convert between metric units!
You try! What is 100 cm in millimeters?
That's right, 100 centimeters is the same as 1000 millimeters! Because milli is 1 space to the right of centi in the chart, we just move the decimal place 1 to the right and add a 0 in its place.
Convert measurements in one metric unit in terms of measurements in another unit, e.g. express measurements in centimeters as measurements in meters.
Convert measurements in one customary unit into measurements in another unit, e.g. express measurements in inches as measurements in feet.
What is Volume?
Finding the volume of an object can help us to determine the amount required to fill that object, like the amount of water needed to fill a bottle, an aquarium or a water tank.
Volume can be considered:
A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
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This is because when we are finding the volume of an object, we are really finding how much space is in the object. For example, if you have a box, and you want to find it's volume, you can fill it up with items in your house so that there is no empty space left. The volume of the box is the same as all of the volume of the items added up. This is the same concept except items in your house, we will fill objects with unit cubes!
Since we are adding up cubes to find volume, our units will be cubic cm, cubic in, and cubic ft.
This video gives an introduction to volume!
Let's learn about how to find volume with unit cubes!
Finding Volume
We can find the volume in 2 ways:
Filling a rectangular prism with unit cubes and adding up the total number of unit cubes, like we learned above!
Second, we can multiply the length, width, and the height. Another way to view this is to multiply the height of the rectangular prism by the area of the base.
The formula for finding volume is V = l × w × h and V = b × h
V stands for volume
l stands for length
w stands for width
h stands for height
b stands for area of the base
Volume is additive!
This means that if we have two rectangular prisms connected to each other and we want to find the area of the entire figure, we can find the volume of each rectangular prism and just add the volumes together!
Let's look at some examples together!
What is the volume of the cube at the below?
We are given the length, width, and height of the cube, so we can use the formula V = l × w × h to find the volume!
The length, width, and height are all 4 cm!
V = 4 cm x 4 cm x 4 cm = 64 cubic cm
Here we are using unit cubes to find the volume of this rectangular prism!
Try these games for more volume practice!
Let's count the number of unit cubes that can fit into a solid to find its volume by playing this game!
Try it! What is the volume of the cube to the above?
That's right! The volume is 18 cubic units because using the formulaV = l × w × h, V = 3 x 2 x 3. This means V = 18 cubic units!