Three-Dimensional Figures Vocabulary • Two-dimensional figures (plane figures) – triangles, quadrilaterals, and circles. They lie in one plane Vocabulary • Three-dimensional figures – figures that have length, width, and depth • Cone • Cylinder • Prism • Pyramid • Sphere • Two-dimensional figures can be transformed through space to create three-dimensional figures. One way is to rotate a two-dimensional figure about a line. This line is sometimes called an axis of symmetry. Space Figures • Translate a rectangle through space – It creates a rectangular prism! Space Figures • Translate a triangle through space – It makes a triangular prism! Space Figures • Translate a circle through space – It makes a cylinder! Space Figures • Rotate a rectangle around an axis of symmetry – it also makes a cylinder! Space Figures • Twirl (rotate) a triangle around one of its sides – It makes a cone! Space Figures • Twirl (rotate) a circle around its diameter – It makes a sphere! Let’s try some examples! Example 1 Solution Example 2 Solution Example 3 A square measures 1 inch on each side. Suppose a copy of the square is translated 2 inches directly above the plane in which it lies to form a second square. The two squares are then connected with four line segments. Describe the three-dimensional figure that is formed. Solution Example 4 Solution Example 5 Turning Point • Let’s test your knowledge! Grab your clicker! 1. What is the figure show below called? 1. 2. 3. 4. Cone Cylinder Cube Rectangular prism 25% 1 25% 25% 2 3 25% 4 2. The base of a cylinder is shaped like a ______. 1. 2. 3. 4. Rectangle Square Triangle circle 25% 1 25% 25% 2 3 25% 4 3. What three-dimensional figure will be formed if the right triangle shown is rotated about the line shown? 1. Cone 25% 25% 25% 25% 2. Cylinder 3. Cube 4. sphere 1 2 3 4 4. What three-dimensional figure will be formed if the rectangle shown is rotated about the line shown? 1. Cone 25% 25% 25% 25% 2. Cylinder 3. Cube 4. sphere 1 2 3 4 5. A rectangle is translated 3 inches directly above the plane in which it lies. The vertices of the two rectangles are then connected with four line segments. What threedimensional figure is formed? 1. 2. 3. 4. Cone Cube Cylinder Rectangular prism 25% 1 25% 25% 2 3 25% 4 6. What three-dimensional figure will be formed if rectangle ABCD is rotated about AB? 1. Cone 25% 25% 25% 25% 2. Cube 3. Cylinder 4. prism 1 2 3 4 Ticket-out-the-door • 1. 2. 3. 4. 5. 6. 7. What 3D figure is created when you…. Translate a rectangle Translate a circle Rotate a rectangle Translate a triangle Rotate a triangle Rotate a circle Translate a square Cross-Sections EQ: How can I describe the cross-sections of solid figures? Vocabulary • Cross-section – a view of the inside of a 3D figure after it is sliced • Polyhedron – a 3D figure (a solid with flat faces) http://www.learner.org/channel/courses/learningmath/geometry/se ssion9/part_c/index.html Example 1 Describe three different cross-sections you can find for the rectangular prism below Solution Example 2 The cylinder below sits on a horizontal base. Draw and describe the cross-section formed when the cylinder is cut by a plane that is tilted away from its base. Solution • The cross-section is shaped like an oval. In mathematics, this shape is called an ellipse. Example 3 • The cone below sits on a horizontal base. Draw and describe the cross-sections formed when the cone is cut by a vertical plane through its vertex. Solution • The cross-section is shaped like an isosceles triangle. The base of the triangle is on the base of the cone. Example 4 • The pyramid below has a square horizontal base. Draw and describe the cross-sections formed when the cone is cut by a vertical plane that does not pass through the vertex at its top. Solution • The cross-section will be shaped like a quadrilateral. This figure is called an isosceles trapezoid. Turning Point • Let’s test your knowledge! Grab your clicker! 1. The cylinder below is cut by the plane shown. What is the shape of the crosssection formed? 1. Circle 25% 25% 25% 25% 2. Rectangle 3. Trapezoid 4. Triangle 1 2 3 4 1. 2. 3. 4. 2. The cube below is cut by the plane shown. What is the shape of the crosssection formed? Circle 25% 25% 25% 25% Rectangle Square triangle 1 2 3 4 3. Suppose a cone is cut by a plane. Which cross-section is NOT possible? 1. 2. 3. 4. Circle Ellipse Square triangle 25% 1 25% 25% 2 3 25% 4 4. The cross-section of a three-dimensional figure is shaped like a circle. The threedimensional figure could NOT be a ________. 25% 25% 25% 25% 1. 2. 3. 4. Cone Cylinder Pyramid sphere 1 2 3 4 5. A cylinder is cut by a plane to form a cross section shaped like an ellipse. How could the plane that formed the cross-section have cut the cylinder? 1. Parallel to a base of the cylinder 2. Perpendicular to a base of the cylinder 3. Slightly tilted away from a base of the cylinder 4. None of the above 25% 1 25% 25% 2 3 25% 4
© Copyright 2024