Exploring Formulas of Three-Dimensional Figures

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Exploring Formulas of Three-Dimensional Figures

• Kari Jung
• Applied Math - Unit 8
• Warner High School

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Rectangular Prisms
h
w
l

• What two-dimensional shapes make up a rectangular
  prism?

• Rectangles

• Which sides are the same?

• Front/Back
• Right/Left
• Top/Bottom

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Rectangular Prisms, cont.

• What is the formula for finding the area of
  each side?
• Front/Back
• l h
• Right/Left
• w h
• Top/Bottom
• l w
• Now put it all together to find total surface
  area of the rectangular prism.
• 2lh 2wh 2lw TSA of rectangular prisms

h
w
l
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Cubes

• A cube is a rectangular prism. What
  specifically do we know about cubes?
• All the sides are the same lengths

s

• What is the area of 1 face?
• s s or s2
• How many faces does a cube have?
• 6 faces
• What is the Total Surface Area of a Cube?
• 6s2 TSA of a cube

s
s
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Cylinders

• What shapes make up a cylinder?

circles rectangle

• How do you find the area of one base?

?r2
2?r
h

• What is the area of the rectangle?

2?rh

• What is the total surface area of the cylinder?

2?r2 2?rh TSA of a cylinder
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Lets Practice

• Imagine the room we are in as a rectangular
  solid, without any windows or doors. Suppose the
  room is 40 feet long, 24 feet wide, and 10 feet
  high. Draw a sketch of the room and find the
  total surface area of the room.
• A number cube has sides that are 3 cm long. Draw
  a sketch of the number cube and find its surface
  area.
• Joe is working on building a silo. It is about
  20 feet in diameter and about 30 feet tall, with
  a cone on top. Draw a sketch and find how much
  metal it will take to make the side of the silo
  only?

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Identify the 3-Dimensional Figures
What 3-dimensional shapes do you see in the
pictures on this page?