Parallel Cross-Sections of Right Prisms
Match Prism to Cross-Section Shape
Draw a line to match each prism to the shape of its parallel cross-section.
Name the Cross-Section
Circle the shape you would see if you sliced each prism parallel to its base.
Triangular prism
Rectangular prism (box)
Hexagonal prism
More Cross-Sections
Circle the correct cross-section shape.
Cylinder
Cube
Pentagonal prism
Octagonal prism
Match Shape to Prism
Draw a line to match each cross-section shape to its prism.
Sort: Prisms and Non-Prisms
Sort each 3D shape into the correct column.
Name the Prism
If the cross-section is the given shape, name the prism.
Cross-section is a triangle → ___ prism
Cross-section is a circle → ___
Cross-section is a rectangle → ___ prism
Cross-section is a pentagon → ___ prism
True or False? Cross-Sections
Circle TRUE or FALSE for each statement.
Every parallel cross-section of a prism is the same shape
A cylinder has a circular cross-section
A triangular prism has a rectangular cross-section
All cross-sections of a rectangular prism are congruent rectangles
More True or False
Circle TRUE or FALSE.
A cone has a uniform cross-section
All prisms have uniform cross-sections
A sphere has a circular cross-section
The cross-section of a cube is always a square
Describe the Cross-Section
For each shape, describe what you would see if you sliced it parallel to the base.
A cube sliced parallel to its base: ___
A triangular prism sliced parallel to its triangular face: ___
A cylinder sliced parallel to its circular base: ___
Cross-Section Properties
Answer each question about cross-sections.
How many faces does a triangular prism have? ___
What shape are the two parallel faces of a hexagonal prism? ___
If you slice a rectangular prism at any height parallel to the base, what shape do you always get? ___
Why does a cone not have a uniform cross-section? ___
Match Prism to Number of Faces
Draw a line to match each prism to its number of faces.
Draw the Cross-Section
Draw the shape of the parallel cross-section for each prism.
A pentagonal prism (draw the cross-section)
An octagonal prism (draw the cross-section)
A right prism with an L-shaped base (draw the cross-section)
Cross-Section Reasoning
Answer each question with a full explanation.
Explain the difference between a cross-section of a prism and a cross-section of a pyramid.
A prism has a cross-section with 6 sides. How many faces does the prism have in total?
Can a prism have a circular cross-section? Explain.
Real-World Cross-Sections
Identify the cross-section shape for each real-world object.
A Toblerone box: ___
A pencil (hexagonal): ___
A log: ___
A shipping container: ___
Home Activity: Slice It!
Explore cross-sections with everyday objects!
- 1Slice a block of cheese parallel to one face. What shape do you see?
- 2Look at a box (cereal box, tissue box). What shape would each slice be?
- 3Find objects shaped like prisms around your home. Name the cross-section of each.
- 4Use playdough to make a triangular prism, then slice it to see the cross-section.
- 5Look at different shaped pencils. What cross-section does each have?
Nets of 3D Shapes
A net is the unfolded version of a 3D shape.
How many faces does a triangular prism have? ___. Draw a simple net: ___
A rectangular prism has 6 faces. How many different nets can you make? (Hint: more than 1)
What shape would the net of a cube look like? Describe it: ___
Properties of 3D Shapes
Complete the table for each prism.
Triangular prism: Faces = ___, Edges = ___, Vertices = ___
Rectangular prism: Faces = ___, Edges = ___, Vertices = ___
Hexagonal prism: Faces = ___, Edges = ___, Vertices = ___
Pentagonal prism: Faces = ___, Edges = ___, Vertices = ___
Euler's Formula
Euler's Formula: Faces + Vertices − Edges = 2. Verify for each shape.
Triangular prism (F=5, V=6, E=9): F + V − E = ___
Cube (F=6, V=8, E=12): F + V − E = ___
Pentagonal prism: F + V − E = ___
Does Euler's formula work for all prisms? ___
Match 3D Shape to Real Object
Draw a line to match each 3D shape to a real-world object.
Sort 3D Shapes by Cross-Section
Sort each 3D shape by the shape of its uniform cross-section.
Front, Top and Side Views
For each 3D shape, describe its front, top, and side views.
A cylinder: Front view = ___. Top view = ___. Side view = ___
A triangular prism: Front view = ___. Top view = ___. Side view = ___
A cube: Front view = ___. Top view = ___. Side view = ___
Identifying Cross-Sections
Circle the correct cross-section for each cut.
Cylinder cut horizontally:
Cylinder cut vertically through centre:
Triangular prism cut perpendicular to length:
Rectangular prism cut diagonally:
Volume of Prisms
Volume of prism = cross-sectional area × length. Calculate each volume.
Triangular prism: Triangle area = 12 cm², length = 8 cm. Volume = ___
Rectangular prism: 5 cm × 4 cm cross-section, length = 10 cm. Volume = ___
L-shaped prism: L-cross-section area = 18 cm², length = 6 cm. Volume = ___
Surface Area of Prisms
Surface area of prism = 2 × (cross-section area) + (perimeter × length).
Triangular prism: triangle has sides 3, 4, 5 cm and area 6 cm². Length = 10 cm. SA = ___
Rectangular prism 5 × 3 × 8 cm. SA = ___
Prism Types in Architecture
This graph shows how many of each prism type are used in a building design. Each icon = 1 prism.
| Rectangular prisms | |
| Triangular prisms (roof) | |
| Cylinders (columns) | |
| Hexagonal prisms (tiles) |
What percentage of shapes are rectangular prisms?
Which type of prism is least common?
What fraction of shapes have a circular cross-section?
3D Shapes in the Classroom
Tally how many of each 3D shape are found in the classroom.
| Item | Tally | Total |
|---|---|---|
Rectangular prisms | ||
Cylinders | ||
Spheres | ||
Other prisms |
Packing Problems
Solve these real-world packing problems using prisms.
How many 2 cm × 2 cm × 2 cm cubes fit in a box 10 cm × 8 cm × 6 cm? ___
A cylinder has radius 5 cm and height 10 cm. Volume = π × r² × h ≈ 3.14 × 25 × 10 = ___
Identifying Prisms in the Real World
For each object, identify the type of prism and describe its cross-section.
A can of beans: type = ___, cross-section = ___
A cheese wedge: type = ___, cross-section = ___
A Toblerone box: type = ___, cross-section = ___
A swimming pool (rectangular): type = ___, cross-section = ___
Drawing 3D Shapes
Use these boxes to sketch each 3D shape.
Draw and label a triangular prism:
Draw and label a hexagonal prism:
3D Shape Reasoning
Answer these reasoning questions.
Why can't a sphere be a prism? ___
A prism with cross-section area 45 cm² and volume 360 cm³. What is its length? ___
Design a prism with volume exactly 100 cm³. Describe its dimensions: ___