3-Dimensional Figures

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3-Dimensional Figures

• Filling Wrapping Notes

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Review of Circles

• Geometry Notes

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Circles

• Circles have two important interior parts
• Diameter
• Radius

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• Radius a line that starts at the center point
  and ends at the border of the circle.
• The radius is half as long as the diameter.
• Diameter a line that passes through the center
  of the circle connecting both sides.
• The diameter is twice as long as the radius.

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Measures of Circles

• There are two different ways to measure Circles
• Circumference
• Area

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• Circumference is the perimeter of the circle or
  the distance around the edge of the circle.
• Area is the amount of space needed to cover the
  circle.

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Using Formulas

• A circular flower bed in Kays backyard has a
  diameter of 8 feet. What is the area of the
  flower bed? Round your answer to the nearest
  tenth.
• What is the circumference of the flower bed?
  Round your answer to the nearest tenth

50.3 ft²
25.1 ft
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Using Formulas

• A company manufactures aluminum lids. The
  radius of each lid is 3 cm. What is the area of
  one lid? Round your answer to the nearest tenth.
• What is the Circumference? Round your answer to
  the nearest tenth

28.3 cm²
18.8 cm
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Using Formulas

• A radio station broadcasts a signal over an area
  with a 75-mile radius. What is the area of the
  region that receives the radio signal? (Round
  your answer to the nearest tenth)

17,671.5 square miles
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Using Formulas

• If the area of a circular mirror is 200.95 m²,
  what is the radius of the mirror? Round your
  answer to the nearest tenth.
• What is the diameter of the mirror?

8 meters
16 meters
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Using Formulas

• The area of a circular frame is 12.56 inches²,
  what is the diameter of the picture? Round your
  answer to the nearest tenth.

4 inches
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Aspects of 3-D figures

• Three-dimensional figures have a length, width,
  and height. They also have faces, edges, bases,
  and vertices (or a vertex).
• Faces The flat surfaces on 3-D figures.
• Bases The top and bottom of the figure where the
  height lies in between.

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• Edges Where the faces meet.
• Vertices Where the edges meet.

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Types of 3-D figures

• There are many types of 3-D figures. There are
• Cubes
• Rectangular Prisms
• Triangular Prisms
• Pyramids
• Cylinders
• Cones

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• Rectangular Prisms Have 6 faces that are all
  rectangles.
• Example a box

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• Cubes Have six faces just like a rectangular
  prism. A cube is a special type of rectangular
  prism because all the faces are congruent
  squares.
• Example Dice

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• Triangular Prisms Have five faces. Its two
  bases are triangles and three of its faces are
  rectangles.
• Example Some tents.

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• Pyramids Have five faces. The base is a
  rectangle the other four faces are triangles.
• Example Pyramids in Egypt.

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• Cylinders Have two bases that are circles.
• Example A can of pop.

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• Cones Have one base that is a circle.
• Example An ice cream cone.

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• There are two different measures of 3-D figures
• VOLUME
• SURFACE AREA

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Measures of 3-D figures

• Volume the amount of material needed to fill an
  object.
• The capacity of a three-dimensional shape.
• Surface Area the amount of material needed to
  wrap an object.
• The area required to cover a three-dimensional
  shape

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Using Formulas

• How much wrapping paper do you need to
  completely cover a rectangle box that is 20
  inches by 18 inches by 2 inches?

872 in²
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Using Formulas

• Each of the cone-shaped cups near the water
  cooler has a radius of 3 centimeters and a height
  of 10 centimeters. If 1 cubic centimeter can
  hold one milliliter of liquid, how much water can
  each cup hold? Round your answer to the nearest
  whole.

94 milliliters
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Using Formulas

• The eight Corinthian columns at the Nation
  Building Museum in Washington D.C., are each 75
  feet high and 8 feet in diameter. What is the
  volume of each column? Round your answer to
  nearest tenth.

3769.9 ft³
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Using Formulas

• A small gift box is shaped like a cube. The box
  measures 1.4 inches on each side. What is the
  volume of the gift box? Round your answer to
  nearest tenth.

2.7 in³
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Using Formulas

• The average stone on the lowest level of the
  Great Pyramid of Egypt was a rectangular prism
  5feet long by 5 feet high by 6 feet deep and
  weighed 15 tons. What is the volume of the
  average casting stone? Round your answer to
  nearest tenth.

150.0 ft³
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Using Formulas

• The Great Pyramid of Egypt has a square base
  that measures 751 feet on each side. They
  pyramid is 481 feet high. What is the volume of
  the Great Pyramid? Round your answer to nearest
  tenth.

120,410.3 ft³
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NETS

• Nets Flat patterns of 3-D figures.
• Cubic Net
• Some boxes are shaped like cubes. A cube is a
  three-dimensional shape with six identical square
  faces. The diagram below shoes one possible flat
  pattern for a cubic box.

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• Rectangular Prism Net
• Triangular Prism Net

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• Pyramid Net
• Cylinder Net

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• Cone Net

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Using Formulas

1. A frying pan has a radius of 14 cm. What is the
   circumference? (Round your answer to the nearest
   tenth of a cm)

88.0 cm
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Using Formulas

1. A round stained-glass window has a circumference
   of 195 inches. What is the radius of the window
   to the nearest inch?

31 inches
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Using Formulas

1. A Susan B. Anthony coin has a diameter of 26.5
   millimeters. What is the area of the coin to the
   nearest hundredth?

551.55 mm²
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Using Formulas

1. A triangular prism has a length of 10 inches, a
   width of 7 inches, and a height of 4 inches.
   What is its volume?

140 inches³
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Using Formulas

1. A travel mug is shaped like a cylinder. It is 9
   cm wide and 15 centimeters tall. Find its
   volume. Leave your answer in terms of pi.

303.75p inches³
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Using Formulas

1. How much wrapping paper do you need to completely
   cover a rectangular box that is 20 inches by 18
   inches by 2 inches?

872 inches²
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Using Formulas

1. A can a peas is 3 inches in diameter and 4.5
   inches tall . What is the surface area of the
   can? What is the area of the label around the
   can? Round both to the nearest tenth.

42.4 in²
56.5 in²