# ﻿Slicing Solids

Warmup

Activity #1

Investigate Cross Section of a Cube, Cylinder, and a Pyramid.

Cube • Move the dot on the angle slider(β) to see the figure from different angles.​
• Move the O slider below to rotate the plane horizontally.​
• Move the Z slider below to rotate the plane vertically.

Cylinder • Check the box that reads Show plane to introduce a plane.​
• Click on Free Moving/Horizon/Vertical to view a vertical or a horizontal plane.​
• Move the slider at the bottom to see movement of the plane(either vertically or horizontally).
• Check the box that shows Show Cross Section.​
• Move the bottom slider slowly, either up and down to see shape of slice.​

Cone • Check the box that reads Show plane.​
• Click on Free Moving/Horizon/Vertical to introduce a slider.​
• Check the box that shows Show Cross Section.
• Move the vertical slider slowly up and down to see shape of slice.

Pyramid

• Check the box that reads Show plane.​
• Click on Free Moving/Horizon/Vertical to introduce a slider.​
• Check the box that shows Show Cross Section.”
• Move the vertical slider slowly up and down to see shape of slice.​
• Move Base slider at the top left to right to see slices of pyramid with different bases.

Activity #2

Naming 3-D Objects. • Click on each shape in the applets below and drag the mouse to show the objects turning in 3D.

Describe the shape as precisely as you can.

Describe the shape as precisely as you can.

Describe the shape as precisely as you can.

Here a a rectangular prism and a pyramid with the same base and same height. Drag the large red point up and down to move the plane through the solids.

(1.) If we slice each solid parallel to its base halfway up, what shape cross sections would we get?
(2.) What is the same about the cross sections?
(3.) What is different?
(4.) If we slice each solid parallel to its base near the top, what shape cross sections would we get?
(5.) What is the same about the cross sections?
(6.) What is different?
(7.) Describe the cross sections that would result from slicing each solid perpendicular to its base.

Activity #3

Investigating Cross section of .

Here below is an applet with a rectangular prism, 4 units by 2 units by 3 units. • Use the sliders to interact with the applet, and then answer the questions that follow.

(1.) Describe the cross section in words: A plane cuts the prism parallel to the bottom and top faces.​

(2.) Describe the cross section in words: The plane moves up and cuts the prism at a different height.​

(3.) Describe the cross section in words: A vertical plane cuts the prism diagonally.

A square pyramid has a base that is 4 units by 4 units. Its height is also 4 units.

(1.) Describe the cross section in words: A plane cuts the pyramid parallel to the base.​

(2.) Describe the cross section in words: A vertical plane cuts the pyramid.

A cube has an edge of length 4.

(1.) Describe the cross section in words: A plane cuts off the corner of the cube.​

(2.) Describe the cross section in words: The plane moves farther from the corner and makes a cut through the middle of the cube.​

Challenge #1

Sort the images into groups that make sense to you. Be prepared to explain your reasoning.

Challenge #2

A cube is cut into two pieces by a single slice that passes through points A, B, and C. What shape is the cross section?

Quiz Time