Cross sections of 3D objects

The  exercise appears under the Geometry Math Mission. This exercise helps visualize two-dimensional information from three-dimensional objects.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the objects that can provide the cross section: This problem describes a particular cross section and provides a list of three-dimensional solids. The student is asked to select all of the objects that can be cut to create the desired cross section.Cso3do1.png
 * 2) Find the cross sections that can be made from the object: This problem provides a given three-dimensional solid. The student is asked to select all of the possible cross sections that can be made by slicing the object.Cso3do2.png

Strategies
Solid geometry reasoning skills are encouraged to ensure success on this exercise.
 * 1) Some general cross section information is provided here:
 * 2) A sphere can only yield circular cross sections.
 * 3) A cone can yield circle, ellipse, and triangle (usually isosceles) cross sections.
 * 4) A cylinder provides circle, ellipse and rectangle cross sections.
 * 5) A cube can provide pentagons, hexagons, and various types of triangles and quadrilaterals.
 * 6) A triangular prism can provide pentagons, rectangles, trapezoids and many types of triangles.
 * 7) Right square pyramids can be cut to make squares, pentagons, isosceles triangles, trapezoids but cannot make non-square rectangles.
 * 8) A special can arise from a cone that has one straight side and a curved side, like a smiley face.

Real-life Applications

 * 1) Finding volumes by rotating shapes about straight lines is an integral calculus techniques that relies on being able to visualize cross sections of three-dimensional objects.
 * 2) Humans see 2-dimensionally, but depth perceptions allows the mind to infer a third dimension.