3-Dimensional 3-Dimensional FiguresFigures

Filling & Wrapping NotesFilling & Wrapping Notes

AspectsAspects of 3-D figures of 3-D figures

Three-dimensional figures have a Three-dimensional figures have a lengthlength, , widthwidth, and , and heightheight. They also have . They also have facesfaces, , edgesedges, , basesbases, and , and verticesvertices (or a (or a vertexvertex).).

Faces:Faces: The flat surfaces onThe flat surfaces on 3-D figures 3-D figures..

Bases:Bases: The top and bottom of the figureThe top and bottom of the figure where the height lies in between.where the height lies in between.

Edges: Edges: Where the Where the faces meetfaces meet..

VerticesVertices: : Where the Where the edges meetedges meet..

Types of 3-D figuresTypes of 3-D figuresThere are many types of 3-D figures. There are many types of 3-D figures.

There are: There are: CubesCubes

Rectangular PrismsRectangular PrismsTriangular PrismsTriangular Prisms

PyramidsPyramids CylindersCylinders

ConesCones

Rectangular Prisms:Rectangular Prisms: Have 6 faces that Have 6 faces that are all rectanglesare all rectangles..

Example: Example: a boxa box

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

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

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

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

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

There are two different measures of 3-D

figures:VOLUME

SURFACE AREA

Measures of 3-D figuresMeasures of 3-D figures

Volume:Volume: the amount of material needed to the amount of material needed to fillfill an object. an object. The capacity of The capacity of a three-dimensional shape.a three-dimensional shape.

Surface Area: Surface Area: the amount of material the amount of material needed needed to to wrapwrap an object an object.. The area required to coverThe area required to cover a three-dimensional a three-dimensional

shapeshape

Using FormulasUsing FormulasHow much wrapping paper do you How much wrapping paper do you

need to completely cover a rectangle need to completely cover a rectangle box that is 20 inches by 18 inches by box that is 20 inches by 18 inches by

2 inches? 2 inches?

872 in²

Using FormulasUsing FormulasEach of the cone-shaped cups near Each of the cone-shaped cups near the water cooler has a radius of 3 the water cooler has a radius of 3

centimeters and a height of 10 centimeters and a height of 10 centimeters. If 1 cubic centimeter can centimeters. If 1 cubic centimeter can hold one milliliter of liquid, how much hold one milliliter of liquid, how much water can each cup hold?water can each cup hold? Round your Round your

answer to the nearest whole.answer to the nearest whole.

94 milliliters

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Using FormulasUsing FormulasThe eight Corinthian columns at the The eight Corinthian columns at the

Nation Building Museum in Nation Building Museum in Washington D.C., are each 75 feet Washington D.C., are each 75 feet

high and 8 feet in diameter. What is high and 8 feet in diameter. What is the volume of each column? the volume of each column? Round Round

your answer to nearest tenth.your answer to nearest tenth.

3769.9 ft³

Using FormulasUsing FormulasA small gift box is shaped like a A small gift box is shaped like a

cube. The box measures 1.4 inches cube. The box measures 1.4 inches on each side. What is the volume of on each side. What is the volume of

the gift box? the gift box? Round your answer to Round your answer to nearest tenth.nearest tenth.

2.7 in³

Using FormulasUsing FormulasThe average stone on the lowest The average stone on the lowest

level of the Great Pyramid of Egypt level of the Great Pyramid of Egypt was a rectangular prism 5feet long was a rectangular prism 5feet long by 5 feet high by 6 feet deep and by 5 feet high by 6 feet deep and

weighed 15 tons. What is the volume weighed 15 tons. What is the volume of the average casting stone? of the average casting stone? Round Round

your answer to nearest tenth.your answer to nearest tenth.

150.0 ft³

Using FormulasUsing FormulasThe Great Pyramid of Egypt has a The Great Pyramid of Egypt has a

square base that measures 751 feet square base that measures 751 feet on each side. They pyramid is 481 on each side. They pyramid is 481

feet high. What is the volume of the feet high. What is the volume of the Great Pyramid? Great Pyramid? Round your answer to Round your answer to

nearest tenth.nearest tenth.

120,410.3 ft³

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NETSNETS

Nets:Nets: Flat patterns Flat patterns of 3-D figuresof 3-D figures..

Cubic Net:Cubic Net: Some boxes are shaped like cubes. A Some boxes are shaped like cubes. A cube cube is a three-is a three-

dimensional shape with six identical square dimensional shape with six identical square facesfaces. The . The diagram below shoes one possible flat pattern for a cubic diagram below shoes one possible flat pattern for a cubic box.box.

Rectangular Prism Net:Rectangular Prism Net:

Triangular Prism Net:Triangular Prism Net:

Pyramid Net:Pyramid Net:

Cylinder Net:Cylinder Net:

Cone Net:Cone Net:

Using FormulasUsing Formulas1.1. A frying pan has a radius of 14 cm. A frying pan has a radius of 14 cm.

What is the circumference? (What is the circumference? (Round Round your answer to the nearest tenth of a cm)your answer to the nearest tenth of a cm)

88.0 cm

Using FormulasUsing Formulas2.2. A round stained-glass window has a A round stained-glass window has a

circumference of 195 inches. What circumference of 195 inches. What is the radius of the window to the is the radius of the window to the nearest inch?nearest inch?

31 inches

Using FormulasUsing Formulas3.3. A Susan B. Anthony coin has a A Susan B. Anthony coin has a

diameter of 26.5 millimeters. What is diameter of 26.5 millimeters. What is the area of the coin to the nearest the area of the coin to the nearest hundredth?hundredth?

551.55 mm²

Using FormulasUsing Formulas4.4. A triangular prism has a length of 10 A triangular prism has a length of 10

inches, a width of 7 inches, and a inches, a width of 7 inches, and a height of 4 inches. What is its height of 4 inches. What is its volume?volume?

140 inches³

Using FormulasUsing Formulas5.5. A travel mug is shaped like a A travel mug is shaped like a

cylinder. It is 9 cm wide and 15 cylinder. It is 9 cm wide and 15 centimeters tall. Find its volume. centimeters tall. Find its volume. Leave your answer in terms of pi.Leave your answer in terms of pi.

303.75π inches³

Using FormulasUsing Formulas6.6. How much wrapping paper do you How much wrapping paper do you

need to completely cover a need to completely cover a rectangular box that is 20 inches by rectangular box that is 20 inches by 18 inches by 2 inches?18 inches by 2 inches?

872 inches²

Using FormulasUsing Formulas7.7. A can a peas is 3 inches in diameter A can a peas is 3 inches in diameter

and 4.5 inches tall . What is the and 4.5 inches tall . What is the surface area of the can? What is the surface area of the can? What is the area of the label around the can? area of the label around the can? Round both to the nearest tenth.Round both to the nearest tenth.

42.4 in² 56.5 in²