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In this lesson, we will explore the concept of volume, recognizing it as an attribute of solid figures. We will also measure volumes by counting unit cubes, and then relate volume to the operations of multiplication and addition in solving word problems.
See the fact file below for more information on the understanding concepts of volume or alternatively, you can download our 27-page Understanding Concepts of Volume worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- When you connect one point to another point, you get a line segment, which is one-dimensional and is only measured by length.
- Two-dimensional shapes, on the other hand, are flat and only have two dimensions – width and height – and are measured by area.
- The objects that we encounter in our day-to-day are solid, three-dimensional objects that have these dimensions: length, width, and depth. Three-dimensional objects are measured by their volume.
FINDING THE VOLUME OF SOLID OBJECTS
- Volume is the amount of space that a solid object takes up.
- Finding the volume of a three-dimensional object is similar to finding the area of two-dimensional objects, but only with one additional dimension to include.
- Cube. To get its volume, we figure out how many cubic units can fit inside it.
- Cubic units are almost like square units, but they have depth.
- A cubic unit is 1 unit high, 1 unit wide, and 1 unit deep.
FINDING THE VOLUME USING UNIT CUBES
- Using the definition of volume, let’s take a look at this example.
- These cubes make up a rectangular prism. The cubes represent the volume of the prism. This prism is five cubes by two cubes by one cube. In other words, it is five cubes long, two cubes high, and one cube wide.
- Therefore, counting all the cubes, this rectangular prism has 10 cubic units.
- Here is another example. Note that the height of the prism will indicate how many layers of cubes are in the prism.
- Counting the cubes of the top layer, we get 20 cubic units.
- Since there are four layers and each has a volume of 20 cubic units, the total volume of the rectangular prism must be 80 cubic units.
FINDING VOLUME AS AREA TIMES LENGTH
- Since counting cubic units would take a long time, we can just use a formula to find the volume of a cube.
- VOLUME = length x width x height
- It doesn’t matter which numbers you multiply first, you’ll still get the same results. From the formula above, it’s just area multiplied to the length.
- Example 3. Let’s find out the volume of this cube.
- Let’s multiply the dimensions to find the volume in cubic meters.
- Volume = length x width x height
- Volume = 6 m x 6 m x 6 m
- Volume = 216 cubic meters
- The volume of the cube is 216 cubic meters.
- Cubic meters can also be written as m³. So, from the above example we can also say that the volume is 216 m³.
- Other units of volume are cubic centimeters (cm³), cubic inches (iin³), cubic feet (ft³), cubic miles (mi³), and cubic kilometers (km³).
- Example 4. Take a look at this box.
- We see that it has three dimensions, so let’s find the volume of the figure on the right.
- Volume = length x width x height
- Volume = 5 ft x 3 ft x 2 ft
- Volume = 30 cubic feet
- The volume of the box is 30 cubic feet or 30 ft³.
FINDING VOLUME AS AREA OF BASE TIMES HEIGHT
- Let’s try to find the volume given the area of the base and the height of a rectangular prism.
- Example 5. The base of a rectangular prism has an area of 8 square meters. The height of the rectangular prism is 5 meters. What is the volume of the rectangular prism?
- We all know that a prism is a shape that looks like we made a stack of exact copies of the base. To find the volume of any prism, we follow this:
- VOLUME = base area x height
- Let’s fill the information we know about the prism.
- volume = base area x height
- volume = 8 square meters x 5 meters
- volume = 40 cubic meters
- Therefore, the volume of the rectangular prism is 40 cubic meters or 40 m³.
Understanding Concepts of Volume Worksheets
This is a fantastic bundle which includes everything you need to know about the understanding concepts of volume across 27 in-depth pages. These are ready-to-use Understanding Concepts of Volume worksheets that are perfect for teaching students about the concept of volume, recognizing it as an attribute of solid figures. We will also measure volumes by counting unit cubes, and then relate volume to the operations of multiplication and addition in solving word problems.
Complete List Of Included Worksheets
- Lesson Plan
- Problems Involving Perimeters
- What’s the Perimeter?
- Counting Time
- What’s the Area?
- Willy Wonka’s Room
- That Star
- Pixels by Pixels
- More Cubes
- Area and Perimeter Problem
- Drawing Perimeters
- Drawing Areas
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Link will appear as Understanding Concepts of Volume Facts & Worksheets: https://kidskonnect.com - KidsKonnect, July 3, 2020
Use With Any Curriculum
These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.