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Understanding Cross Sections

This document defines and provides examples of cross sections. A cross section is the two-dimensional shape revealed when a plane cuts through a three-dimensional object. Common examples given include cutting an orange in half to reveal a circular cross section, floor plans showing cross sections of houses, and MRI images displaying cross sections of the body. The document outlines how cross sections can be cut parallel or perpendicular to an object's base, and provides the two-dimensional shapes that would result from cutting various three-dimensional geometric shapes in different ways.

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315 views17 pages

Understanding Cross Sections

This document defines and provides examples of cross sections. A cross section is the two-dimensional shape revealed when a plane cuts through a three-dimensional object. Common examples given include cutting an orange in half to reveal a circular cross section, floor plans showing cross sections of houses, and MRI images displaying cross sections of the body. The document outlines how cross sections can be cut parallel or perpendicular to an object's base, and provides the two-dimensional shapes that would result from cutting various three-dimensional geometric shapes in different ways.

Uploaded by

api-294079637
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Cross Sections

What you see when you slice.

What is a Cross Section?


So far we have dealt with two-dimensional
figures and three-dimensional figures
independently (more or less), but cross
sections are where the two shall meet.
A cross section is the two-dimensional figure
that results or that is revealed when a twodimensional plane intersects with a threedimensional figure.

Cross Section
Another way of saying it: a cross section is
the shape you see on the inside when you slice
off a piece of a figure.
Cutting an orange in half is a good example.
When you slice the orange in half and then
look at the new face you just made, what is its
shape?
A circle.

Cross Sections all Around


Cross Sections are all around us, everywhere.
There is a cross section when you cut your
birthday cake.
There are cross sections in every loaf of
sliced bread.
A floor plan of a house is nothing but a fancy
cross section.
Science books and advertisements are full of
them.

More Cross Sections


Cross sections let us see what is on the
inside.
MRI images are good examples.
Mall maps are also examples.
Can you think of some examples of cross
sections that you have seen and how or why
they are used?

Theres more than One Way to


slice a Figure.
There is an infinite number of ways that a
two-dimensional plane can intersect with a
three-dimensional figure. For this
presentation, the following will be
demonstrated:
Intersections Parallel with the base.
Intersections Perpendicular with the base.

Clarifying Terms
An intersection perpendicular to the
base will be exactly straight up and
down have 900 angles where the twodimensional plane meets the threedimensional base.
How do you remember what
perpendicular is?

Clarifying Terms
An intersection parallel to the base is a side
to side cut that is parallel to the base of the
three-dimensional figure. It will always yield a
two-dimensional figure in the shape of the
base.
Remember: Parallel means that if the twodimensional plane and the base of the figure
went on forever, they would never, ever touch
(intersect).
Lets look at some cross sections.

A Cross Section Parallel to the


base of a Cylinder gives us what
two- dimensional shape?

A Circle

A Cross Section Perpendicular to the


base of a Cylinder gives us what twodimensional shape?

A Rectangle

A Cross Section Perpendicular to the


base of a Pyramid gives us what twodimensional shape?

A Triangle

A Cross Section Parallel to the base


of a Square Pyramid gives us what
two- dimensional shape?
A Square

A Cross Section Perpendicular to the


base of a Rectangular Prism gives us
what two- dimensional shape?

A Rectangle

A Cross Section Parallel to the base of a


Rectangular Prism gives us what twodimensional shape?

A Rectangle

A Cross Section Perpendicular to the


base of a Cone gives us what twodimensional shape?

A Triangle

A Cross Section Parallel to the base of


a Cone gives us what two-dimensional
shape?

A Circle

Finally, no matter how you slice it, the


cross section of a sphere is going to be
a .

A Circle

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