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Three-Dimensional Figures

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Vocabulary Two-dimensional figures (plane figures) – triangles, quadrilaterals, and circles. They lie in one plane

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Vocabulary Three-dimensional figures – figures that have length, width, and depth Cone Cylinder Prism Pyramid Sphere

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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.

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Space Figures Translate a rectangle through space – It creates a rectangular prism!

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Space Figures Translate a triangle through space – It makes a triangular prism!

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Space Figures Translate a circle through space – It makes a cylinder!

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Space Figures Rotate a rectangle around an axis of symmetry – it also makes a cylinder!

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Space Figures Twirl (rotate) a triangle around one of its sides – It makes a cone!

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Space Figures Twirl (rotate) a circle around its diameter – It makes a sphere!

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Let’s try some examples! Example 1

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Solution

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Example 2

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Solution

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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.

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Solution

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Example 4

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Solution

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Example 5

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Turning Point Let’s test your knowledge! Grab your clicker!

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1. What is the figure show below called? 1.Cone 2.Cylinder 3.Cube 4.Rectangular prism

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2. The base of a cylinder is shaped like a ______. 1.Rectangle 2.Square 3.Triangle 4.circle

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3. What three-dimensional figure will be formed if the right triangle shown is rotated about the line shown? 1.Cone 2.Cylinder 3.Cube 4.sphere

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4. What three-dimensional figure will be formed if the rectangle shown is rotated about the line shown? 1.Cone 2.Cylinder 3.Cube 4.sphere

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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 three- dimensional figure is formed? 1.Cone 2.Cube 3.Cylinder 4.Rectangular prism

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6. What three-dimensional figure will be formed if rectangle ABCD is rotated about AB? 1.Cone 2.Cube 3.Cylinder 4.prism

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Ticket-out-the-door What 3D figure is created when you…. 1.Translate a rectangle 2.Translate a circle 3.Rotate a rectangle 4.Translate a triangle 5.Rotate a triangle 6.Rotate a circle 7.Translate a square

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Cross-Sections EQ: How can I describe the cross-sections of solid figures?

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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

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Example 1 Describe three different cross-sections you can find for the rectangular prism below

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Solution

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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.

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Solution The cross-section is shaped like an oval. In mathematics, this shape is called an ellipse.

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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.

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Solution The cross-section is shaped like an isosceles triangle. The base of the triangle is on the base of the cone.

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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.

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Solution The cross-section will be shaped like a quadrilateral. This figure is called an isosceles trapezoid.

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Turning Point Let’s test your knowledge! Grab your clicker!

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1. The cylinder below is cut by the plane shown. What is the shape of the cross- section formed? 1.Circle 2.Rectangle 3.Trapezoid 4.Triangle

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2. The cube below is cut by the plane shown. What is the shape of the cross- section formed? 1.Circle 2.Rectangle 3.Square 4.triangle

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3. Suppose a cone is cut by a plane. Which cross-section is NOT possible? 1.Circle 2.Ellipse 3.Square 4.triangle

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4. The cross-section of a three-dimensional figure is shaped like a circle. The three- dimensional figure could NOT be a ________. 1.Cone 2.Cylinder 3.Pyramid 4.sphere

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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

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