Period: Date Lesson 2: Common 3-Dimensional Shapes and Their Cross- Sections

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Percival Pope
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1 : Common 3-Dimensional Shapes and Their Cross- Sections Learning Target: I can understand the definitions of a general prism and a cylinder and the distinction between a cross-section and a slice. Warm Up Geo CC Regents : Linda is designing a circular piece of stained glass with a diameter of 7 inches. She is going to sketch a square inside the circular region. To the nearest tenth of an inch, find the largest possible length of a side of the square. Definition of Prism A general prism is cylinder in which two bases are equal polygons in parallel planes, and all other faces are parallelograms. There are two types of prism; oblique prism and right prism. Oblique prism is when the axis is not to the base. Right prism if the axis is to the base. In right prism, all lateral areas are.

Terms Definitions Drawing Base (Base Face) Edge Vertex Lateral faces The two congruent, parallel sides of a prism A segment that is formed By the intersection Of two faces of

Cross Section When the slice is parallel to the base.

2 Terms Definitions Drawing Base (Base Face) Edge Vertex Lateral faces The two congruent, parallel sides of a prism A segment that is formed By the intersection Of two faces of a solid. A point where three or more edges of A solid intersect. The faces in a geometric solid that are not the bases. Slice A general intersection a plane and a solid. Cross Section When the slice is parallel to the base. Definition of Cylinder A General Cylinder is 3 dimensional solid in which two faces are parallel bases and the lateral area is in the shape of a rectangle. cylinder: A general cylinder whose lateral edges are to a circular base cylinder: A general cylinder whose lateral edges are not to a circular base

3 Example 1. Sketch the cross-section of the cylinder below Example 2.Sketch the figures formed if the rectangular regions are rotated around the provided axis A pyramid is a solid figure that has a polygon base and the lateral faces are all triangles that meet at a point Rectangular pyramid is a pyramid with a rectangular base General cone is solid figure with a circular base and a single vertex. Example 3. Sketch the cross-section of the cylinder below Example 4. Sketch the figures formed if the rectangular regions are rotated around

Hemisphere 3-D Solids Sketch each figure Sketch the Cross-section 1.

4 Spheres and Hemispheres Every point on the sphere, is the same distance from the origin in space The cross-section of a sphere is always a Each half of a sphere is called a Hemisphere 3-D Solids Sketch each figure Sketch the Cross-section 1. A regular pyramid with a square base 2. A wooden cube 3. A cone 4. An oblique cylinder 5. An oblique cylinder

5 6. Water tower in the shape of a cylinder 7. Triangular prism 8. Rectangular prism 9. Hemisphere tank Example 6. Ann buys a block of clay for a Geometry project. The block is shaped like a cylinder with a base area of 48π cm 2, and the height is three times the radius. Ann decides to cut the block of clay into two pieces. She places a wire across the diameter of the circular base as shown in the figure. Then, she pulls the wire straight down to create 2 congruent chunks of clay. Ann wants to keep one chunk of clay for later use. To keep that chunk from drying out, she wants to place a piece of plastic sheeting on the surface she exposed when she cut through the cylinder. Describe the newly exposed two-dimensional cross section, and find its area. Round your answer to the nearest whole square inch. Show your work.

6 : Common 3-Dimensional Shapes and Their Cross- Sections Problem Set 1. Sketch the cross-section for the following figures: a. b. c. d. 2. Draw the cross-section or the slice a. b. c. 3. Sketch the figures formed if the rectangular regions are rotated around the provided axis a. b.

7 4. Draw the cross-section or the slice a. b. c. 5. Which figure can have the same cross section as a sphere? PARCC-type question: 6. Rick buys a block of clay for a Geometry project. The block is shaped like a rectangular prism with length edges of 12 in, width edges of 6 in, and height edges of 5 in. Rick decides to cut the block of clay into two pieces. He places a wire across the diagonal of the front face of the prism as shown in the figure. Then, he pulls the wire straight back to create 2 congruent chunks of clay. Rick wants to keep one chunk of clay for later use. To keep that chunk from drying out, he wants to place a piece of plastic sheeting on the surface he exposed when he cut through the prism. Describe the newly exposed two-dimensional cross section, and find its area. Round your answer to the nearest whole square inch. Show your work.

Cross Sections of Three-Dimensional Figures

Domain 4 Lesson 22 Cross Sections of Three-Dimensional Figures Common Core Standard: 7.G.3 Getting the Idea A three-dimensional figure (also called a solid figure) has length, width, and height. It is