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Slicing 3D figures
Slicing-3d-figures 256
Description
Exercise Name: Slicing 3D figures
Math Missions: 7th grade (U.S.) Math Mission, High school geometry Math Mission
Types of Problems: 3

The topic Slicing 3D figures appears under the 7th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise helps visualize 2D cross sections of 3D solids.

Types of Problems

There are three types of problems in this exercise:

  1. Find shape of slice: This problem provides a three-dimensional solid and a pink slicing plane. The user is asked to visualize what kind of shape the slice will provide.
    S3df1

    Find shape of slice

  2. Find shape that gives slice: This problem provides a two-dimensional slice of a solid. The problem asks the user to determine which solid the slice could have come from.
    S3df2

    Find shape that gives slice

  3. Draw a cross section: This problem provides a three-dimensional solid and a directional cross section. The user is asked to sketch a possible cross section on the grid provided.
    S3df3

    Draw a cross section

Strategies

Three dimensional geometric reasoning and manipulation are required to do this exercise accurately and efficiently.

  1. It is possible to make a chart keeping track of the cross sections from each solid. For example, perpendicular 2D cross sections of a cylinder will always provide rectangles or circles.
  2. The manipulative on Draw a cross section is generally forgiving. Also, since any cross section is acceptable choosing one with convenient values would increase efficiency.

Real-life Applications

  1. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.
  2. Architects use lots of geometry when building bridges, roofs on houses, and other structures.
  3. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.

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