G.GMD.4 ACTIVITY #7
-
PATTERSON
7
cRoss sEcTtoNs
A cross section is the face that is formed when you make a slice through an object.
We create cross sections every time we cut a slice of cheese from the cheese
block. Most of these cheese cross sections are squares (if we cut them just right).
Another example of cross section cuts would be these triangles. When we slice
the cross section parallel to the base of this triangular prism we get copies of the base. A
cross section cannot contain any piece of the original face - it all comes from 'inside' the
solid. ln this picture only the grey piece is the cross section. As demonstrated by the cross
section of this cube not all cross sections needs to be parallel to a face. ln this activity we are
going to investigate the cross sections of a cube.
PRED!CITIONS
Before beginning this activity make predictions on which of the following cross sections are possible for a
cube. Place a check mark in the box beside the polygons that you feel are possible cross sections.
X
x
x
K
)(
K
Square
Rectangle
Rhombus
Parallelogram
Trapezoid
f,
f,
[f
.Y
equilateralTriangle
Pentagon
ff
Scalene Triangle
lsosceles Triangle
Hexagon
E,:::;
nigr,t Triangle
Cli,.r"
lsosceles Trapezoid
ACTIVITY
(1) Go to:
http://www. shodo r. o rglinte ractivate/activities/C rossSectio
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lver/
(2) Set the Cross Section Grapher to a PRISM with 4
Lateral Faces (A cube)
(3) Manipulate the sliders to create the different
cross sections. When you find one of the polygons
mentioned above record it on the record sheet. Use
the grid to help you determine what the shape you
have created.
(4) Create as many of the polygons cross sections as
you can.
J.SLIDERS TO CONTROL
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RECORDING RESULTS (Draw and shade
the cross section that matches the given polygon.)
Rhombus
I
I
Parallelogram
lsosceles Trapezoid
n
Scalene Triangle
Equilateral Triangle
lsosceles Triangle
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Right Triangle
Pentapon
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G.GMD.4 ACflVffY #7
-
PATTERSON
QUESTIONS
1. A couple of the shapes on the cross section list were impossible. Explain what makes them impossible.
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2. What is the maximum number of sides of the polygon
cross section for a rectangular prism? Explain.
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3. Given the two points, plot two other points that would create the required cross section. Label the
diagram to help explain why it is the required cross section.
c) lsosceles Triangle
b) lsosceles
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d) Equilateral Triangle
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4. Given a triangular pyramid, what cross section could you create? List them.
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G.GMD,4 ACTIVITY #7
- PATTERSON
4
5. Given a hexagonal prism, create an octagonal cross section.
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5. Jennifer says that you can create a rectangle as a cross section for a
chance!!-
Cross
cylinder. Rex laughs.... "Not
sections of cylinders are circles and ellipses!!!" Who is right? Explain.
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