Introduction to Solid Geometry

Name ______Module 3

Introduction to Solid Geometry

Learning Target: I can identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Opening Exercise

Identify the shape of each 3-dimensional solid.

Solid Geometry

Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face. An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection of three or more faces.

A cubeis a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.

A netis a diagram of the surfaces of a three-dimensional figure that can be folded to form the three-dimensional figure. To identify a three-dimensional figure from a net, look at the number of faces and the shape of each face.

Describe the three-dimensional figure that can be made from the given net.

A cross sectionis the intersection of a three-dimensional figure and a plane.

Describe each cross section.

Classify each figure and identify the shape of the base.

1.2.

3.4.

Describe the three-dimensional figure that can be made from the given net.

5.6.

Describe each cross section.

7. 8.

Name ______Module 3

Introduction to Solid GeometryProblem Set

1. A rectangle will be rotated 360 about a line which contains the point of intersection of its diagonals and is parallel to a side. What three dimensional shape will be created as a result of the rotation?

(1) a cube

(2) a rectangular prism

(3) a cylinder

(4) a sphere

2. The figure in the diagram below is a triangular prism. Which statement must be true?

1) /
2) /
3) /
4) /

3.The diagram below shows a rectangular prism. Which pair of edges are segments of lines that are coplanar?

1) / and
2) / and
3) / and
4) / and

4. The diagram below shows a right pentagonal prism. Which statement is always true?

1) /
2) /
3) /
4) /

5. Sketch the cross-section for the following figures:

a. / b. / c. / d.

6. The lateral faces of a regular pyramid are composed of

1) / squares / 3) / congruent right triangles
2) / rectangles / 4) / congruent isosceles triangles

7. Which piece of paper can be folded into a pyramid?

1) / / 3) /
2) / / 4) /

8. A roll of candy is shown in the accompanying diagram. Which solid can best describe the shape of the candy?

9.Triangle ABC represents a metal flag on pole AD, as shown in the accompanying diagram. On a windy day the triangle spins around the pole so fast that it looks like a three-dimensional shape. Which shape would the spinning flag create?

Name ______Module 3

Introduction to Solid GeometryExit Ticket

1. Is this a cylinder? Explain why or why not.

2. For each of the following cross-sections, sketch the figure from which the cross-section was taken.