Checklist and Assignment
Notes
Checklist:
Grade
Regions: Rectangles, triangles, circles.
Solids: Rectangular Solids, cylinder
Review of perimeter, area, and volume.
Scaling in three-dimensions
Assignment:
1. Table 10.2 on p 557, table 10.3 on p 559
2. p 563 Quick Quiz 6 - 10
3. p 563 - 566 7, 9, 14, 41, 47, 50, 54, 57, 61, 65 - 67,
75
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Key Words
Notes
Grade
Perimeter
Area
Volume
Scaling Laws
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Grades
Notes
It is common to describe steepness in terms other than
with the angle of incline. For instance a road on a hill
with 30% grade expresses the slope, the rise over run, as a
percentage. That is 30/100 is 30%.
What grade (percent) is used to describe a hill that rises
up by 6 feet for each 20 foot run?
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Common Two-Dimensional Arguments
Notes
For a circle, all points are located the same distance from
the center - the radius. The diameter is twice this
distance, which means the distance across a cicle on a line
through the center is the diameter.
Another common two-dimesional object is the polygon - a
closed shape with straigth edges.
Properties include perimeter (or circumference for circles)
as the length of the boundary, and area.
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Example - Perimeter
Notes
A window consists of a 4-foot by 6-foot rectangle capped
by a semicircle. How much trim is needed to go around
the window? (What is the perimeter?)
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Example - Area
Notes
A stairwell in a newly built home needs the space beneath
the stairs to be covered with plywood. The stairs are 9 ft
high and 12 ft wide. What is the area of the region?
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Three-Dimensional Geometry
Notes
Volume and surface area are two important properties of
three-dimensional objects. Formulas of surface area
should have square lengths, or sums of squared length for
each side. Volumes should have cubed lengths.
A cylinder, for instance, has a volume where the area of
the circular base πr 2 is multiplied by the height h. The
surface area is found by a clever trick: Imagine cutting
and unfolding the cylinder to be shaped like a rectangular
sheet. The length of the sheet is the circumference of the
base, 2πr and the height of the sheet is h, so the area of
the surface is 2πrh.
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Example - Application
Notes
Which holds more soup? A can with a diameter of 3
inches and a height of 4 inches, or a can with a diameter
of 4 inches and a height of 3 inches?
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Scaling Laws
Notes
1. Lengths scale with the scale factor.
2. Areas scale with the square of the scale factor.
3. Volumes scale with the cube of the scale factor.
Ex: A model car is made with a scale factor of 10. The
actual car will be 10 times as long, 10 times as wide, and
10 times as tall. How will the surface area (meaningful for
paint) and the volume (meaningful for interior space) of
the actual car scale?
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Example - Scaling Laws
Notes
Suppose, somewhat magically, your size suddenly doubled
(height, weight, depth).
For each of the following, either length, area, or volume is
mentioned.
By what factor has your waist size increased?
How much more material would be required for clothing?
By what factor will your weight change?
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Notes
Notes