11-2A Visualize Cross-Sections
of Solids
Name
Objective
To describe the two-dimensional figures that result from slicing
three-dimension figures
Cynthia and Rob are slicing blocks of cheese to add to a snack tray for
a family party. Cynthia places her knife perpendicular to the side of
the cheese as she slices. Rob angles his so it is not perpendicular as he
slices. Are the slices the same shape? If not, how are they different?
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
! To visualize and compare how the slices or cross-sections look, think
of the blocks of cheese as rectangular prisms with square bases.
Key Concept
A cross-section is the plane
figure made by the intersection
of a three-dimensional figure by
a plane.
Rob’s Slices
Cynthia’s Slices
So, the slices are different shapes. Cynthia’s slices are squares, while Rob’s slices
are rectangles.
! You can also slice other three-dimensional shapes, such as a pyramid or
a cylinder to form different cross-sections.
What shapes, or plane figures, are made by horizontal, vertical, and diagonal
cross-sections of a triangular prism?
Horizontal Cross-Section
Visualize a slice of the prism
from side to side and parallel
to the bases.
Vertical Cross-Section
Visualize a slice of the prism
that is perpendicular to
both bases.
Diagonal Cross-Section
Visualize a slice of the
prism that starts and ends
between edges and is not
perpendicular to the bases.
It is a triangle.
It is a rectangle.
It is a trapezoid.
Notice that the shape of the cross-section of a triangular prism depends
on how you cut the figure.
So, depending on how the triangular prism is sliced, triangles, rectangles,
and trapezoids are some shapes that can be formed by the cross-sections.
Sketch the figure and then describe the cross-section.
1. Square pyramid; vertical cross-section.
2. Square prism; diagonal cross-section.
3. Discuss and Write There are many ways to position the vertical cross-section
of a triangular prism. How do the resulting shapes compare with each other?
Use after SourceBook Lesson 11-2.
Chapter 11, Lesson 2A
1
11-2A Visualize Cross-Sections
of Solids
Name
Compare and contrast each cross-section.
4.
5.
Figure A
Figure B
Figure C
Figure C
Sketch the figure. Then draw and describe the cross-section.
6. Square pyramid; diagonal
cross-section.
7. Rectangular pyramid;
vertical cross-section.
8. Cylinder; vertical
cross-section.
Use the following information for exercises 9–12.
Toby read that several two-dimensional shapes can be formed using a
cross-section of a cone. Show how he can cut each cone to form the shape listed.
9. Circle
11. Figure shaped like an O that is not a circle.
10. Triangle
12. Figure shaped like a D
CRITICAL THINKING
13. The cross-section formed by cutting a cone from its vertex to its
base is the same shape as the one formed by cutting a square
pyramid from its top vertex to its base. How can this be if a cone
has round surfaces and a pyramid has flat surfaces?
2
Chapter 11, Lesson 2A
Use after SourceBook Lesson 11-2.
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
Figure A
Figure B