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.Cone 2.Cylinder 3.Cube 4.Rectangular prism

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

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

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

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

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

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

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) 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 cross- section formed? 1.Circle 2.Rectangle 3.Trapezoid 4.Triangle

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

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

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

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