Polyhedron 10.1 POLYHEDRONS, PRISMS, AND PYRAMIDS. A solid made up of Polygons. face. edge. vertex
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1 10.1 POLYHEDRONS, PRISMS, AND PYRAMIDS Polyhedron Definition A solid made up of Polygons Picture/Example face edge vertex prefix for a polyhedron Gives you the number of faces on the polyhedron. Tetrahedron, Pentahedron, Hexahedron, Heptahedron,.Icosahedron(20),. regular polyhedron All faces are congruent 1
2 Prism Polyhedron consisting of two congruent parallel bases. Every other face is created by connecting corresponding vertices. bases of a prism lateral faces of a prism lateral edges of a prism triangular prism rectangular prism hexagonal prism trapezoidal prism get the idea right prism oblique prism The parallel congruent faces The faces that are not the bases. The side faces The edges that are not a part of the base. The side edges. The bases are triangles The bases are rectangles The bases are The bases are The lateral edges are perpendicular with the bases The lateral edges are not perpendicular with the bases.
3 Pyramid base of a pyramid lateral face of a pyramid lateral edge of a pyramid vertex of a pyramid altitude of a pyramid The length of the line segment perpendicular to the base to the vertex height of a pyramid Altitude of the pyramid 1-2 Draw the following: 1. A triangular right prism with regular bases. 2. A tetrahedron with regular triangular faces. 3. A box measuring 3 inches on each edge is below. How many 1 inch cubes will fit in it. 3
4 Solids with curved surfaces Definition Picture/Example Sphere radius center hemisphere great circle All the points equidistant from a given point in space The distance from the center of the sphere to the sphere. The point that all points on the sphere are equidistant from. Half a sphere. The circle formed by cutting a sphere in half. Cylinder bases axis radius right cylinder oblique cylinder altitude A solid formed by extending a circle along an axis The circle A line segment through the center of the bases The distance from the center of the circle to the circle A cylinder where the axis is perpendicular to the bases A cylinder where the axis is not perpendicular to the bases The length of the axis from base to base.
5 Cone base radius vertex right cone oblique cone altitude A solid with a circle for a base and every line segment from the base ends at a common point The circle at the bottom of the cone is the base The radius of the base The peak of the cone A cone where the line segment connecting the vertex with the center of the circle is perpendicular with the base A non-right cone The perpendicular line segment connecting the vertex with the base. Find the shape that best describes the real object given: 1. Die 2. Can of soup 3. box of cereal 4. A half moon 5. What would a triangle look like if you spun it about the axis as shown? 5
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7 10.2 VOLUME OF PRISMS AND CYLINDERS Volume is measure of the amount of space contained in a solid. (3 dimensional measure) Basically the number of unit cubes you can fit in a solid. 3 3 this is 1 in this is 1cm Why do we call the above a cubic inch and a cubic centimeter? 1. How many inch cubes can you fit in the shape below? I need you to draw it and use the inch cubes. 3 in 5 in 2 in 2. What is the volume of the shape below. a) b) 7
8 The volume of a Prism is ( area of the base) height BH VPr ism H Number of these Area =L X W This works for cylinders as well. (use the chips) H V = A = X H V cylinder ( area of the base) height BH This is the same for oblique prisms and cylinders. V prism or cylinder ( oblique or right) ( area of the base) height BH
9 4. Find the volume of the prisms and cylinders. First draw a picture of the base. a) 7 ft 6 ft 4 ft b) 6 ft 3 ft 4 ft 8 ft c) 4 ft 10 ft 5. Volume = 6.Volume = 9
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11 10.3 VOLUME OF PYRAMIDS AND CONES V pyramid or cone 1 ( area of the base) height BH Start by drawing a picture of the base and find the base's area. 1. Volume = 2. Apothem 11 cm Volume 3. The volume of the cone is 1408 cubic feet. r 11
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13 10.4 VOLUME PROBLEMS 1. Find the volume. All angles are right angles. Measurements are in meters. Volume = 2. Find the volume between the cylinders. Volume = 3. Find the volume of a square-based pyramid. The height of the pyramid is 9 cm and the length of each side of the square base is 7 cm. Volume = 4. If you cut a 2 inch square out of each corner of an X piece of paper (the lined paper in your 2 folder) and fold it into a box leaving the top of the box open, then what is the volume of the box? 5. The height of a cone is 3 ft and the volume of the cone is 102 cubic ft. What is the radius of the base of the cone? 13
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15 10.5 DISPLACEMENT AND DENSITY Displacement is an objects volume. It is the amount of space an object displaces. You can find the volume of an irregular shaped object by dropping it in a prism or cylinder filled with water and measure its displacement (the volume of water displaced). example: Find the volume of the apple. volume of the = EX 1/ Let's say that the apple was dropped into a cylinder with radius 4 inches and displaced 2.2 inches of watter. What is the volume of the apple? EX 2/ A piece of metal is dropped into a square based prism with side length 7 inches. The piece of metal displaced 3.5 inches of whater. What is the volume of the piece of metal. EX 3/ A hunk of mysterious metal is dropped into a glass square-based prism, 3 cm on each edge, causing the water level to rise 1.8 cm. What is the volume of the object. 15
16 Mass is defined as the amount of matter an object has. Weight mass of an object is the mass on earth, it s weight. Density = the mass of matter in a given volume(weight per cubic unit) What we are looking for is the mass of each or depending on what are measurements are. Ex. If the density of a dog is 4.2 lbs/ cubic foot, then the weight of a dog with a volume of 1 cubic foot is 4.2 lbs. Density = Weight of the object Number of cubesyou can shoveintotheobject mass volume EX1/ If the previous apple had a mass of 4 oz. What is it's density Density = volume mass = = oz in 3 EX2/ A hunk of mysterious metal is dropped into a glass square-based prism, 3 cm on each edge, causing the water level to rise 1.8 cm. What is the density of the object if it has a mass of45 grams? (Express your answer in grams/cm 3, accurate to three decimal places.) Density = EX3/ The density of Gold is g/ cubic centimeter. If a block of gold is 10 cm by 8 cm by 4 cm, then what is it's mass?
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18 10.6 VOLUME OF A SPHERE Vsphere 3 4 r V hemisphere 3 1. Volume = 2. What is the volume of the sliced hemisphere shown below? Volume = 3. Diameter = 4. A giant scoop, operated by a crane, is in the shape of a hemisphere of radius 21 inches. The scoop is filled with molten hot steel. When the steel is poured into a cylindrical storage tank of diameter 28 inches, the molten steel will rise to a height of how many inches? Height =
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20 10.7 SURFACE AREA OF A SPHERE SA sphere 2 4 r SA hemisphere Top + Base 1. Surface area = 2. Surface area = 2 36 in. Find the Volume of the sphere. 3. radius = 4 cm. Find the volume.
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Volume of Prisms and Cylinders Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit
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UNIT 12 Volume and Surface Area 2016 2017 CCM6+ Name: Math Teacher: Projected Test Date: Main Concept(s) Page(s) Vocabulary 2 Basics of 3-D Figures 3 8 Volume of Rectangular Prisms and Finding Missing