Cross Sections of a Solid Figure

In solid geometry, the cross section of a three-dimensional object is a two-dimensional figure obtained by slicing
the object perpendicular to its axis and viewing it end on.

In other words, a cross section of a solid is a plane figure obtained by the intersection of that solid with a plane.
The cross section of an object therefore represents an infinitesimal "slice" of a solid, and may be different
depending on the orientation of the slicing plane.

Let's observe some common solids and their cross sections. Note that only the part with a darker shade is
thecross section.

Cube

A square cross section can be created by slicing the cube by a plane parallel to one of its sides.

An equilateral triangle cross section can be obtained by cutting the cube by a plane defined by the midpoints of the
three edges emanating from any one vertex.

Triangular Prism

A prism has the same cross section all along its length. A triangular prism has a triangle cross section all along its length.

Pyramids

If the pyramid is cut with a plane (green) parallel to the base, the intersection of the pyramid and the plane is a
square cross section (red).

Sphere

Any cross section of a sphere will be a circle.

Try these questions

1. What cross section can you get from this figure when you cut parallel to the base?

   

   1. Rectangle

   2. Trapezoid

   3. Ellipse

   4. Circle

2. What about when you cut vertically? (Use the figure from Question 1)

   1. Rectangle

   2. Square

   3. Ellipse

   4. Circle

3. When cut diagonally? (Use the figure from Question 1)

   1. Rectangle

   2. Square

   3. Ellipse

   4. Circle

ANSWERS TO PRACTICE TEST QUESTIONS

1. D.          Circle.

   




2. A.         Rectangle

   




3. C.         Ellipse

   

FINAL TEST QUESTIONS

1. Use the figure below to answer Questions 1 – 2. A piece of cheese is a prism with equilateral triangular bases.
   How can you slice the cheese to make an equilateral triangle?

   

   1. Cut at an angle

   2. Cut perpendicular to the bases

   3. Cut parallel to the bases




2. A rectangle?

   1. Cut at an angle

   2. Cut perpendicular to the bases

   3. Cut parallel to the bases




3. A cross section is the face that results from slicing through a solid shape. True or False?

   Answer: True




4. You can get an ellipse from a cross section of a sphere. True or False?

   Answer: False.




5. Describe the cross section below.

   

   1. The cross section is a trapezoid.

   2. The cross section is a pentagon.

   3. The cross section is a pentagonal pyramid.




6. Describe the cross section below.

   

   1. The cross section is a circle.

   2. The cross section is a small sphere.

   3. The cross section is a point.

ANSWERS TO FINAL TEST QUESTIONS

1. C

2. B

3. TRUE

4. FALSE

5. B

6. C