Unit 4D:2-3 Dimensional Shapes

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Unit 4D2-3 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.

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3-Dimensional Shapes
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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).

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face
cube
vertex
edge
A cube, just like a rectangular prism, has 6
faces (all squares), 8 vertices, and 12 edges.
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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. Lets view
some examples
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Rectangular prism
face
base
edge
vertex
A rectangular prism has 6 faces, 8 vertices,
and 12 edges.
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Triangular prism
base
base
face
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.
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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. Lets view
some examples
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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.
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vertex
Triangular pyramid
face
base
A triangular pyramid has four faces. All faces,
including its base, are triangles. It has six
edges and four vertices.
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vertex
Cone
height
radius
base
A cone is an object that has a circular base and
one vertex
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Cylinder
height
base
radius
A cylinder is a solid object with two identical
flat ends that are circular. It also has one
curved side.
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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.
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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.
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Now its your turn to identify the
three-dimensional shapes we have discussed.
Complete the following worksheet ONLY identifying
what each shape is.
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Volume of a Cube

• The formula for finding Volume of a Cube is V
  e³

e
e
e
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Practice

• Find the volume of a cube with sides 12cm.

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Practice

• What is the volume of a cube with sides 4.5in?

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Surface Area of a Cube

• The formula for finding Surface Area of a Cube
  is SA 6e²

e
e
e
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Practice

• Find the surface area of a cube with sides 6cm.

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Practice

• What is the surface area of a cube with sides
  5.5in?

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Now its your turn to calculate the volume and
surface area of a cube. Complete the following
worksheet on both sides.
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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
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Introduction

• The following video will show you an introduction
  on how to calculate the volume of a right prism.
• Volume of a Right Prism

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Practice
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Practice
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Now its your turn to calculate the volume of a
right prism. Complete the following worksheet
stopping when you reach lesson 12-4.