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3-Dimensional Figures Filling & Wrapping Notes

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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 PyramidsCylindersCones

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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 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. 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. Example: Pyramids in Egypt.

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

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Cones: Have one base that is a circle. Example: An ice cream cone. 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. 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 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. 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 2.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 3.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 4.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 5.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. 303.75 π inches³

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Using Formulas 6.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 7.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

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