Embedded Files
Lesson overview
Lesson overview
In this lesson you will:
explore surface area of rectangular prisms
learn about faces and nets of rectangular prisms
determine smallest surface area for a given volume in a rectangular prism
apply these ideas to other types of prisms.
Before you start - Surface area refresh
Before you start - Surface area refresh
The surface area of a solid is the material needed to make the solid. Below is an image of a rectangular prism and its net.
The surface area can be found by adding the areas together. A rectangular prism is made up of 6 rectangular faces, so the surface area would be:
Surface Area = Area 1 + Area 2 + Area 3 + Area 4 + Area 5 + Area 6
Activity 1 - Faces of a rectangular prism
Activity 1 - Faces of a rectangular prism
Task 1
Task 1
The faces of a rectangular prism can be collapsed into a two-dimensional net.
Open the Desmos interactive, Surface Area of a Rectangular Prism in a new tab by clicking on the image.
(If the folder tab is open on the left hand side of the screen close it so you can see the graph in full screen.)
Use the activity to calculate the areas of the six rectangular faces and add them to find the surface area.
Write your working in your exercise book or folder.
Use the sliders in the Desmos activity to check your answers.
Task 2
Task 2
The rectangular prism you can see in the image has been broken into a net.
Complete the interactive by dragging the correct measurements onto each of the edges of the net.
Did you notice?
Did you notice?
Hopefully you have noticed that each of the faces is repeated, and there are actually only three different rectangles in the entire prism.
Activity 2 - Same volume, different surface area
Activity 2 - Same volume, different surface area
The three rectangular prisms below have the same volume.
Volume
4 × 4 × 4 = 64 cubic cm
Volume
2 × 4 × 8 = 64 cubic cm
Volume
16 × 4 × 1 = 64 cubic cm
In your exercise book or folder, calculate the surface area of each prism.
Activity 3 - Smallest surface area
Activity 3 - Smallest surface area
When making any container or object, we want the surface area to be small, because it costs money the build the container or object. What can we do to a rectangular prism to make the surface area smaller?
Open the Desmos interactive, Minimum Surface Area in a new tab by clicking on the image.
(If the folder tab is open on the left hand side of the screen close it so you can see the graph in full screen.)
Adjust the dimensions of the rectangular prism with volume 36 cubic cm.
Can you make the surface area the smallest it can be?
What do you need to do to achieve this?
Test your theory by changing the volume and trying again.
Did you notice?
Did you notice?
Fact: For a rectangular prism of any volume, the smallest surface area will occur when all measurements are equal (a cube).
Activity 4 - Other prisms
Activity 4 - Other prisms
How can we break down a triangular prism and cylinder?
Open the Desmos interactive, Surface Area of a triangular prism and cylinder in a new tab by clicking on the image.
(If the folder tab is open on the left hand side of the screen close it so you can see the graph in full screen.)
Use the switches to view which parts of the net match with which parts of the prism.
Draw the prism in your exercise book or folder and calculate the surface area.
Check your calculations of surface area in the Desmos activity.
Use the switch in the top right hand corner to swap to a cylinder and repeat Steps 2-4.
Activities too easy?
Activities too easy?
Can you make a triangular prism or a cylinder that has a volume of 64 cubic cm and a surface area smaller than our 4 cm by 4 cm by 4 cm cube?
Explore this problem using the Lesson 3 challenge activity Google Doc.
Click on the link to open a new tab and view the Google Doc.
Click on the Use Template button to create a copy for you to edit.
Handing in your work
Handing in your work
Don't forget to hand in the work you completed today!
Your teacher will have told you to do one of the following:
Upload any digital documents you created and any photos you took of your written work to your Learning Management system (MS Teams, Google Classroom for example).
Email any digital documents you created and any photos you took of your written work to your teacher.
Make sure you keep any hand written work you did in your exercise book or folder as your teacher may need to see these when you are back in class.
Student reflection
Student reflection
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