It has six flat sides and all angles are right angles.
And all of its faces are rectangles.
It is also a prism because it has the same cross-section along a length. In fact it is a rectangular prism.
Examples of Cuboids
Cuboids are very common in our world, from boxes to buildings we see them everywhere. You can even fit them inside other cuboids!
A box with a slot cut as a handle
Cuboids in a cuboid room
Boxes for model trains
Now that's just silly!
Volume and Surface Area
The volume of a cuboid is found using the formula:
Volume = Height × Width × Length
Which is usually shortened to:
V = h × w × l
Or more simply:
V = hwl
The volume of the following solids are often required to solve real world problems involving quantity, capacity, mass and strength of materials including liquids.
Volume of a Cube
Example 25
Find the volume of a cube of side 4 cm.
Solution:
Surface Area
And the surface area is found using the formula:
A = 2wl + 2lh + 2hw
Example: Find the volume and surface area of this cuboid.
In this interactive geometry investigation, students explore geometric solids and their properties. Specifically, students count the number of faces, edges, and corners (vertices) in various solids.
Learning Objectives
Students will:
analyze characteristics and properties of three-dimensional geometric shapes
count the number of faces, edges, and corners (vertices) in various geometric solids
As students are exploring the various geometric solids, begin a class discussion which includes the following points.
Students should note the following characteristics:
Each solid has flat sides called faces.
Each solid has edges to connect the faces.
Each solid has corners that connect the edges. (Note that the activity sheet refers to corners as "vertices", so you may wish to familiarize students with this vocabulary.)
If you have these shapes in your classroom, have students find the shapes that match those in this computer activity.
This lesson is designed to help students focus on the properties of each shape. The tools allow them to color the faces, edges, or corners (vertices) easily by holding the shift key while clicking the mouse on the paint palette and then on a face. (The edges are always white and the corners black.)
Teacher Note: For today's lesson, students will only complete the table on the activity sheet. Save the three questions below the table for tomorrow's lesson.
As students complete the activity sheet, guide them as needed. For example, when asking "How many sides does each face have?", guide the student to click the given face, and color the sides. When determining the number of faces, it may be helpful to color the faces and count as they color. (It's interesting to observe students doing this: some color all faces the same color, while others color the faces different colors.)
After determining the number of faces, students are asked to count the number of edges and vertices (corners) in the solid. Before actually counting the number of edges, students may wish to "guess" the number.
For example, working with the dodecahedron, a student may say each face has five sides — a pentagon. She counts 12 faces. In guessing the number of edges, she may estimate 60 and give as her reason, "5 sides × 12 faces = 60 edges." Counting the edges with the result of 30 provided an opportunity to have her take a second look at the dodecahedron and find out why. (Each edge is shared by two faces.)
Taking advantage of opportunities such as these enriches student understanding.
Questions for Students
When you guessed the number of edges in a particular solid, were you correct? Did this affect how you guessed and counted the number of edges in the other solids?
[Student responses may vary. Note that students should use their incorrect guesses to inform future predictions.]
Assessment Options
Collect the students' activity sheets to assess student understanding. Answers to the activity sheet are available.
