Three-Dimensional Figures
Vocabulary
• Two-dimensional figures (plane figures) –
triangles, quadrilaterals, and circles. They
lie in one plane
Vocabulary
• Three-dimensional figures – figures that
have length, width, and depth
• Cone
• Cylinder
• Prism
• Pyramid
• Sphere
• Two-dimensional figures can be
transformed through space to create
three-dimensional figures. One way is to
rotate a two-dimensional figure about a
line. This line is sometimes called an axis
of symmetry.
Space Figures
• Translate a rectangle through space – It
creates a rectangular prism!
Space Figures
• Translate a triangle through space – It
makes a triangular prism!
Space Figures
• Translate a circle through space – It
makes a cylinder!
Space Figures
• Rotate a rectangle around an axis of
symmetry – it also makes a cylinder!
Space Figures
• Twirl (rotate) a triangle around one of its
sides – It makes a cone!
Space Figures
• Twirl (rotate) a circle around its diameter –
It makes a sphere!
Let’s try some examples!
Example 1
Solution
Example 2
Solution
Example 3
A square measures 1 inch on each side.
Suppose a copy of the square is translated 2
inches directly above the plane in which it lies
to form a second square. The two squares are
then connected with four line segments.
Describe the three-dimensional figure that is
formed.
Solution
Example 4
Solution
Example 5
Turning Point
• Let’s test your knowledge! Grab your
clicker!
1. What is the figure show
below called?
1.
2.
3.
4.
Cone
Cylinder
Cube
Rectangular prism
25%
1
25%
25%
2
3
25%
4
2. The base of a cylinder is
shaped like a ______.
1.
2.
3.
4.
Rectangle
Square
Triangle
circle
25%
1
25%
25%
2
3
25%
4
3.
What three-dimensional figure will be
formed if the right triangle shown is rotated
about the line shown?
1. Cone
25%
25%
25%
25%
2. Cylinder
3. Cube
4. sphere
1
2
3
4
4. What three-dimensional figure will be
formed if the rectangle shown is rotated
about the line shown?
1. Cone
25%
25%
25%
25%
2. Cylinder
3. Cube
4. sphere
1
2
3
4
5. A rectangle is translated 3 inches directly above the
plane in which it lies. The vertices of the two rectangles
are then connected with four line segments. What threedimensional figure is formed?
1.
2.
3.
4.
Cone
Cube
Cylinder
Rectangular prism
25%
1
25%
25%
2
3
25%
4
6. What three-dimensional figure will be
formed if rectangle ABCD is rotated about
AB?
1. Cone
25%
25%
25%
25%
2. Cube
3. Cylinder
4. prism
1
2
3
4
Ticket-out-the-door
•
1.
2.
3.
4.
5.
6.
7.
What 3D figure is created when you….
Translate a rectangle
Translate a circle
Rotate a rectangle
Translate a triangle
Rotate a triangle
Rotate a circle
Translate a square
Cross-Sections
EQ: How can I describe the
cross-sections of solid figures?
Vocabulary
• Cross-section – a view of the inside of a
3D figure after it is sliced
• Polyhedron – a 3D figure (a solid with flat
faces)
http://www.learner.org/channel/courses/learningmath/geometry/se
ssion9/part_c/index.html
Example 1
Describe three different cross-sections you can
find for the rectangular prism below
Solution
Example 2
The cylinder below sits on a horizontal base.
Draw and describe the cross-section
formed when the cylinder is cut by a plane
that is tilted away from its base.
Solution
• The cross-section is shaped like an oval.
In mathematics, this shape is called an
ellipse.
Example 3
• The cone below sits on a horizontal base.
Draw and describe the cross-sections
formed when the cone is cut by a vertical
plane through its vertex.
Solution
• The cross-section is shaped like an
isosceles triangle. The base of the triangle
is on the base of the cone.
Example 4
• The pyramid below has a square
horizontal base. Draw and describe the
cross-sections formed when the cone is
cut by a vertical plane that does not pass
through the vertex at its top.
Solution
• The cross-section will be shaped like a
quadrilateral. This figure is called an
isosceles trapezoid.
Turning Point
• Let’s test your knowledge! Grab your
clicker!
1. The cylinder below is cut by the plane
shown. What is the shape of the crosssection formed?
1. Circle
25%
25%
25%
25%
2. Rectangle
3. Trapezoid
4. Triangle
1
2
3
4
1.
2.
3.
4.
2. The cube below is cut by the plane
shown. What is the shape of the crosssection formed?
Circle
25%
25%
25%
25%
Rectangle
Square
triangle
1
2
3
4
3. Suppose a cone is cut by a plane. Which
cross-section is NOT possible?
1.
2.
3.
4.
Circle
Ellipse
Square
triangle
25%
1
25%
25%
2
3
25%
4
4. The cross-section of a three-dimensional
figure is shaped like a circle. The threedimensional figure could NOT be a
________.
25%
25%
25%
25%
1.
2.
3.
4.
Cone
Cylinder
Pyramid
sphere
1
2
3
4
5. A cylinder is cut by a plane to form a cross
section shaped like an ellipse. How could the
plane that formed the cross-section have cut the
cylinder?
1. Parallel to a base of the
cylinder
2. Perpendicular to a base
of the cylinder
3. Slightly tilted away from
a base of the cylinder
4. None of the above
25%
1
25%
25%
2
3
25%
4