Unit 4D:2-3 Dimensional
Shapes
LT5: I can identify three-dimensional figures.
LT6: I can calculate the volume of a cube.
LT7: I can calculate the surface area of a cube.
LT8: I can calculate the volume of a right prism.
LT9: I can identify the two-dimensional shape formed by
slicing a three-dimensional figure.
3-Dimensional Shapes
Three-dimensional figures are not flat figures. They
have length, width, and height. They are also called
solid geometric figures.
The flat surfaces of three-dimensional
figures are called faces.
 The faces meet at edges.
 The edges are line segments.
 The edges meet at vertices (plural of
vertex).

cube
face
vertex
edge
A cube, just like a rectangular prism,
has 6 faces (all squares), 8 vertices, and
12 edges.
A prism is named based on what type of
base you start with. For example, if you
start with a rectangle on the base (bottom)
you will have constructed a rectangular
prism. If you start with a triangle on the
base (bottom) you will have constructed a
triangular prism.
Let’s view some examples…
Rectangular prism
edge
face
base
vertex
A rectangular prism has 6 faces, 8 vertices, and
12 edges.
Triangular prism
base
face
base
face
vertex
A triangular prism has five faces. Its base is a triangle.
(Notice that even when the triangular prism sits on
a rectangle, the base is still a triangle.) Two of its
faces are triangles; three of its faces are rectangles. It has
six vertices and nine edges.
Just like with prisms, pyramids are also
named based on what type of base you start
with. For example, if you start with a
rectangle on the base (bottom) you will
have constructed a rectangular pyramid. If
you start with a triangle on the base
(bottom) you will have constructed a
triangular pyramid.
Let’s view some examples…
Rectangular pyramid
face
vertex
base
A rectangular pyramid has 5 faces. Its base is a
rectangle or a square and the other 4 faces are
triangles. It has 8 edges and 5 vertices.
Triangular pyramid
vertex
face
base
A triangular pyramid has four faces. All faces,
including its base, are triangles. It has six edges
and four vertices.
Cone
vertex
height
base
radius
A cone is an object that has a circular base and
one vertex
Cylinder
height
base
radius
A cylinder is a solid object with two identical flat
ends that are circular. It also has one curved
side.
Sphere
A sphere is an object shaped like a ball. Every
point on the surface of the sphere is the same
distance from the center.
You will now join with a partner to
“create” some 3-D shapes. You will be
given a table to fill in based on the
creation you make. You will be finding
the number of faces, edges, and vertices
of different pyramids and prisms.
Complete the entire table. We will then
discuss your findings as a group.
Now it’s your turn to
identify the threedimensional shapes we
have discussed. Complete
the following worksheet
ONLY identifying what each
shape is.
Volume of a Cube
The formula for finding Volume of a Cube is:
V = e³
e
e
e
Practice
Find the volume of a cube with sides 12cm.
Practice
What is the volume of a cube with sides
4.5in?
Surface Area of a Cube
The formula for finding Surface Area of a
Cube is: SA = 6e²
e
e
e
Practice
Find the surface area of a cube with sides
6cm.
Practice
What is the surface area of a cube with
sides 5.5in?
Now it’s your turn to
calculate the volume and
surface area of a cube.
Complete the following
worksheet on both sides.
Volume of a Right Prism


A right prism is a prism that has its bases perpendicular
to its lateral surfaces. The lateral surfaces (faces that
are NOT the bases) must be rectangles to be a right
prism.
The formula for finding Volume of a Right Prism is:
V = Bh (B is the area of the base)
Lateral
surface
Lateral
surface
Introduction

The following video will show you an
introduction on how to calculate the
volume of a right prism.

Volume of a Right Prism
Practice
Practice
Now it’s your turn to
calculate the volume of a
right prism. Complete the
following worksheet
stopping when you reach
lesson 12-4.