219r. Identifying Prisms and Cylinders
Learning Intentions
- Recognise right prisms and cylinders in diagrams and contexts.
- Identify bases, heights, faces and curved surfaces.
- Choose relevant measurements for surface area and volume problems.
- Draw and fold nets of prisms and cylinders
Pre-requisite Summary
- A prism has two congruent, parallel bases joined by side faces.
- A right prism has side faces that meet the bases at right angles.
- A cylinder has two congruent, parallel circular bases and one curved surface.
- Height is the perpendicular distance between the two bases.
- Surface area requires measurements of all outside surfaces.
- Volume requires the area of the base and the perpendicular height.
- The volume of a prism can be found using
. - The volume of a cylinder can be found using
. - A net is a flat pattern that can be folded to form a three-dimensional object.
- A cylinder net is made from two circles and one rectangle.
Worked Examples
Worked Example 1
A cereal box is shaped like a rectangular prism.
a) Identify the two bases.
b) Identify the side faces.
c) Explain why the object is a right prism.
Worked Example 2
A can of soup is shaped like a cylinder.
a) Identify the bases.
b) Identify the curved surface.
c) Identify the height.
Worked Example 3
A tent is shaped like a triangular prism.
a) Identify the triangular bases.
b) Identify the rectangular faces.
c) State which measurement would represent the prism height.
Worked Example 4
For the rectangular prism shown with length
a) Volume
b) Surface area
Worked Example 5
A cylinder has radius
Select the measurements needed to find:
a) Volume
b) Curved surface area
c) Total surface area
Worked Example 6
A triangular prism has a triangular base with base length
a) Identify the base shape.
b) Identify the perpendicular height of the triangular base.
c) Identify the length of the prism.
Worked Example 7
Construct a net for a rectangular prism with dimensions:
Label all faces before folding.
Worked Example 8
Construct a net for a cylinder with radius
The rectangle in the net should have height
Problems
Problem 1
A tissue box is shaped like a rectangular prism.
a) Identify the two bases.
b) Identify the side faces.
c) Explain why the object is a right prism.
Problem 2
A drink can is shaped like a cylinder.
a) Identify the bases.
b) Identify the curved surface.
c) Identify the height.
Problem 3
A chocolate bar packet is shaped like a triangular prism.
a) Identify the triangular bases.
b) Identify the rectangular faces.
c) State which measurement would represent the prism height.
Problem 4
For a rectangular prism with length
a) Volume
b) Surface area
Problem 5
A cylinder has radius
Select the measurements needed to find:
a) Volume
b) Curved surface area
c) Total surface area
Problem 6
A triangular prism has a triangular base with base length
a) Identify the base shape.
b) Identify the perpendicular height of the triangular base.
c) Identify the length of the prism.
Problem 7
Construct a net for a rectangular prism with dimensions:
Label all faces before folding.
Problem 8
Construct a net for a cylinder with radius
The rectangle in the net should have height
Exercises
Understanding and Fluency
Exercise 1
For each object, state whether it is best modelled as a right prism, cylinder or neither.
a) Shoe box
b) Water pipe
c) Soccer ball
d) Toblerone packet
Exercise 2
A rectangular prism has dimensions:
a) Identify a possible pair of bases.
b) Identify the height between those bases.
c) State the shape of each side face.
Exercise 3
A cylinder has radius
a) Identify the two bases.
b) Identify the curved surface.
c) State the measurement that gives the perpendicular height.
Exercise 4
A triangular prism has triangular bases and three rectangular side faces.
a) Name the bases.
b) Name the side faces.
c) Explain why it is a prism.
Exercise 5
For the rectangular prism with dimensions
a) Volume
b) Surface area
Exercise 6
For a cylinder with diameter
a) Volume
b) Curved surface area
c) Total surface area
Exercise 7
A rectangular prism has dimensions:
a) Draw a labelled net.
b) Label opposite faces with matching dimensions.
c) State how many rectangles are in the net.
Exercise 8
A cylinder has radius
a) Draw the two circular bases.
b) Draw the rectangle for the curved surface.
c) Label the rectangle length as
Reasoning
Exercise 9
Explain why a cube is a type of right prism.
Exercise 10
Explain why the height of a prism must be perpendicular to the bases.
Exercise 11
A student says:
“The curved surface of a cylinder is one of its bases.”
Explain the error.
Exercise 12
A student uses the slanted side length of a triangular prism as the height for volume.
Explain why this may be incorrect.
Exercise 13
Explain why the rectangle in a cylinder net must have length equal to the circumference of the circular base.
Problem-solving
Exercise 14
A box manufacturer wants to make a rectangular prism package with dimensions:
a) Identify the measurements needed for volume.
b) Identify the measurements needed for surface area.
c) Describe what shapes would appear in the net.
Exercise 15
A label is wrapped around the curved surface of a cylindrical jar with radius
a) Identify the shape of the label when unwrapped.
b) State the height of the label.
c) State the length of the label in terms of
Exercise 16
A triangular prism package has a triangular base with base length
a) Select the measurements needed for volume.
b) State the area expression for the triangular base.
c) Describe the faces needed in the net.
Exercise 17
A student folds a net with two congruent circles and one rectangle.
a) Name the solid formed.
b) Identify the bases.
c) Identify the curved surface.
Potential Misunderstandings
- Thinking every three-dimensional object with flat faces is a prism.
- Confusing the base of a prism with the bottom face only.
- Forgetting that a prism has two congruent, parallel bases.
- Confusing the height of a prism with a slanted edge.
- Thinking a cylinder has rectangular faces instead of one curved surface.
- Forgetting that the curved surface of a cylinder becomes a rectangle in the net.
- Using diameter instead of radius in
. - Selecting unnecessary measurements when solving volume problems.
- Omitting hidden or opposite faces when constructing nets.
- Drawing nets that cannot fold because faces are not connected correctly.